case study question on probability

Class 10 Maths Case Study Questions Chapter 15 Probability

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Case study Questions in the Class 10 Mathematics Chapter 15  are very important to solve for your exam. Class 10 Maths Chapter 15 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 10 Maths Case Study Questions  Chapter 15  Probability

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Probability Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 15 Probability

Case Study/Passage-Based Questions

Question 1:

Answer: (a) 18

(ii) If the probability of distributing dark chocolates is 4/9, then the number of dark chocolates Rohit has, is

Answer: (c) 24

(iii) The probability of distributing white chocolates is

Answer: (d) 2/9

(iv) The probability of distributing both milk and white chocolates is

Answer: (b) 5/9

(v) The probability of distributing all the chocolates is

Answer: (b) 1

Question 2:

Rahul and Ravi planned to play Business ( board game) in which they were supposed to use two dice.

1. Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8?

Answer: b) 5/36

2. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13?

Answer: d) 0

3. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12?

Answer: a) 1

4. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7?

Answer: c) 1/6

5. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8?

Answer: d) 5/18

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 15 Probability with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Probability Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case Study on Probability Class 12 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Probability Class 12 Maths can use this page to download the PDF file. 

The case study questions on Probability are based on the CBSE Class 12 Maths Syllabus, and therefore, referring to the Probability case study questions enable students to gain the appropriate knowledge and prepare better for the Class 12 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Probability Class 12 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Probability, therefore, they prepared a set of solutions along with the case study questions on Probability.

The case study on Probability Class 12 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Probability case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Probability Case Study Questions on Class 12 Maths?

There are three major reasons why one should solve Probability case study questions on Class 12 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 12 Maths students, therefore, it is important to solve Probability Case study questions as it will help better prepare for the Class 12 board exam preparation.
• Develop Problem-Solving Skills: Class 12 Maths Probability case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 12 students develop their problem-solving skills, which are essential for success in any profession rather than Class 12 board exam preparation.
• Understand Real-Life Applications: Several Probability Class 12 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Probability as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Probability?

Students can choose their own way to answer Case Study on Probability Class 12 Maths, however, we believe following these three steps would help a lot in answering Class 12 Maths Probability Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Probability questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Probability Class 12 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 12 Probability?

 A few essential things to know to solve Case Study Questions on Class 12 Probability are -

• Basic Formulas of Probability: One of the most important things to know to solve Case Study Questions on Class 12 Probability is to learn about the basic formulas or revise them before solving the case-based questions on Probability.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 12 Maths Probability case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Probability Class 12 Maths?

Use Selfstudys.com to find Case Study on Probability Class 12 Maths. For ease, here is a step-wise procedure to download the Probability Case Study for Class 12 Maths in PDF for free of cost.

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CBSE Class 10 Maths Case Study Questions for Chapter 15 - Probability (Published by CBSE)

Cbse class 10 maths case study questions for chapter 15 - probability are published by the cbse board itself to help students understand the new format of questions. these questions are important for the cbse class 10 maths 2022 board exam preparations..

CBSE Class 10 Maths Case Study Questions for Chapter 15 - Probability are provided here. These questions are quite useful to understand how real-life problems can be put in the form of questions. These case study questions are published by the CBSE board. Solve all these questions to prepare for your exams and score the desired marks.

Case Study Questions for Class 10 Maths Chapter 15 - Probability:

CASE STUDY 1:

On a weekend Rani was playing cards with her family. The deck has 52 cards. If her brother drew one card.

1. Find the probability of getting a king of red colour.

Answer: a) 1/26

2. Find the probability of getting a face card.

Answer: d) 3/13

3. Find the probability of getting a jack of hearts.

4. Find the probability of getting a jack of hearts.

Answer: a) 3/13

5. Find the probability of getting a jack of hearts.

Answer: d) 1/4

CASE STUDY 2:

Rahul and Ravi planned to play Business ( board game) in which they were supposed to use two dice.

1. Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8?

Answer: b) 5/36

2. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13?

Answer: d) 0

3. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12?

Answer: a) 1

4. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7?

Answer: c) 1/6

5. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8?

Answer: d) 5/18

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

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Computational Probability and Statistics

7 case study, 7.1 objectives.

• Use R to simulate a probabilistic model.
• Use basic counting methods.

7.2 Introduction to probability models

In this second block of material we will focus on probability models. We will take two approaches, one is mathematical and the other is computational. In some cases we can use both methods on a problem and in others only the computational approach is feasible. The mathematical approach to probability modeling allows us insight into the problem and the ability to understand the process. Simulation has a much greater ability to generalize but can be time intensive to run and often requires the writing of custom functions.

This case study is extensive and may seem overwhelming, do not worry we will discuss these ideas again in the many lessons we have coming up this block.

7.3 Probability models

Probability models are an important tool for data analysts. They are used to explain variation in outcomes that cannot be explained by other variables. We will use these ideas later in this text to help us make decisions about our statistical models.

Often probability models are used to answer a question of the form “What is the chance that …..?” This means that we typically have an experiment or trial where multiple outcomes are possible and we only have an idea of the frequency of those outcomes. We use this frequency as a measure of the probability of a particular outcome.

For this block we will focus just on probability models. To apply a probability model we will need to

• Select the experiment and its possible outcomes.
• Have probability values for the outcomes which may include parameters that determine the probabilities.
• Understand the assumptions behind the model.

7.4 Case study

There is a famous example of a probability question that we will attack in this case study. The question we want to answer is “In a room of \(n\) people what is the chance that at least two people have the same birthday?”

Exercise : The typical classroom at USAFA has 18 students in it. What do you think the chance that at least two students have the same birthday? 62

7.4.1 Break down the question

The first action we should take is to understand what is being asked.

• What is the experiment or trial?
• What does it mean to have the same birthday?
• What about leap years?
• What about the frequency of births? Are some days less likely than others?

Exercise : Discuss these questions and others that you think are relevant. 63

The best first step is to make a simple model, often these are the only ones that will have a mathematical solution. For our problem this means we answer the above questions.

• We have a room of 18 people and we look at their birthdays. We either have two or more birthdays matching or not; thus there are two outcomes.
• We don’t care about the year, only the day and month. Thus two people born on May 16th are a match.
• We will ignore leap years.
• We will assume that a person has equal probability of being born on any of the 365 days of the year.
• At least two means we could have multiple matches on the same day or several different days where multiple people have matching birthdays.

7.4.2 Simulate (computational)

Now that we have an idea about the structure of the problem, we next need to think about how we would simulate a single classroom. We have 18 students in the classroom and they all could have any of the 365 days of the year as a birthday. What we need to do is sample birthdays for each of the 18 students. But how do we code the days of the year?

An easy solution is to just label the days from 1 to 365. The function seq() does this for us.

Next we need to pick one of the days using the sample function. Note that we set the seed to get repeatable results, this is not required.

The first person was born on the 228th day of the year.

Since R works on vectors, we don’t have to write a loop to select 18 days, we just have sample() do it for us.

What do we want R to do? Sample from the numbers 1 to 365 with replacement, which means a number can be picked more than once.

Notice in our sample we have at least one match, although it is difficult to look at this list and see the match. Let’s sort them to make it easier for us to see.

The next step is to find a way in R for the code to detect that there is a match.

Exercise : What idea(s) can we use to determine if a match exists?

We could sort the data and look at differences in sequential values and then check if the set of differences contains a zero. This seems to be computationally expensive. Instead we will use the function unique() which gives a vector of unique values in an object. The function length() gives the number of elements in the vector.

Since we only have 17 unique values in a vector of size 18, we have a match. Now let’s put this all together to generate another classroom of size 18.

The next problem that needs to be solved is how to repeat the classrooms and keep track of those that have a match. There are several functions we could use to include replicate() but we will use do() from the mosaic package because it returns a data frame so we can use tidyverse verbs to wrangle the data.

The do() function allows us to repeat an operation many times. The following template

where {stuff to do} is typically a single R command, but may be something more complicated.

Load the libraries.

Let’s repeat for a larger number of simulated classroom, remember you should be asking yourself:

What do I want R to do? What does R need to do this?

This is within 2 decimal places of the mathematical solution we develop shortly.

How many classrooms do we need to simulate to get an accurate estimate of the probability of a match? That is a statistical modeling question and it depends on how much variability we can accept. We will discuss these ideas later in the semester. For now, you can run the code multiple times and see how the estimate varies. If computational power is cheap, you can increase the number of simulations.

7.4.3 Plotting

By the way, the method we have used to create the data allows us to summarize the number of unique birthdays using a table or bar chart. Let’s do that now. Note that since the first argument in tally() is not data then the pipe operator will not work without some extra effort. We must tell R that the data is the previous argument in the pipeline and thus use the symbol . to denote this.

Figure 7.1 is a plot of the number of unique birthdays in our sample.

Figure 7.1: Bar chart of the number of unique birthdays in the sample.

Exercise : What does it mean if the length of unique birthdays is 16, in terms of matches? 64

7.4.4 Mathematical solution

To solve this problem mathematically, we will step through the logic one step at a time. One of the key ideas that we will see many times is the idea of the multiplication rule. This idea is the foundation for permutation and combinations which are counting methods frequently used in probability calculations.

The first step that we take is to understand the idea of 2 or more people with the same birthday. With 18 people, there are a great deal of possibilities for 2 or more birthdays. We could have exactly 2 people with the same birthday. We could have 18 people with the same birthday, We could have 3 people with the same birthday and another 2 people with the same birthday but different from the other 3. Accounting for all these possibilities is too large a counting process. Instead, we will take the approach of finding the probability of no one having a matching birthday. Then the probability of at least 2 people having a matching birthday is 1 minus the probability that no one has a matching birthday. This is known as a complementary probability. A simpler example is to think about rolling a single die. The probability of rolling a 6 is equivalent to 1 minus the probability of not rolling a 6.

We first need to think about all the different ways we could get 18 birthdays. This is going to be our denominator in the probability calculation. First let’s just look at 2 people. The first person could have 365 different days for their birthday. The second person could also have 365 different birthdays. So for each birthday of the first person there could be 365 birthdays for the second. Thus for 2 people there are \(365^2\) possible sets of birthdays. This is an example of the multiplication rule . For 18 people there are \(365^{18}\) sets of birthdays. That is a large number. Again, this will be our denominator in calculating the probability.

The numerator is the number of sets of birthdays with no matches. Again, let’s consider 2 people. The first person can have a birthday on any day of the year, so 365 possibilities. Since we don’t want a match, the second person can only have 364 possibilities for a birthday. Thus we have \(365 \times 364\) possibilities for two people to have different birthdays.

Exercise: What is the number of possibilities for 18 people so that no one has the same birthday.

The answer for 18 people is \(365 \times 364 \times 363 ... \times 349 \times 348\) . This looks like a truncated factorial. Remember a factorial, written as \(n!\) with an explanation point, is the product of successive positive integers. As an example \(3!\) is \(3 \times 2 \times 1\) or 6. We could write the multiplication for the numerator as \[\frac{365!}{(365-n)!}\] As we will learn, the multiplication rule for the numerator is known as a permutation .

We are ready to put it all together. For 18 people, the probability of 2 or more people with the same birthday is 1 minus the probability that no one has the same birthday, which is

\[1 - \frac{\frac{365!}{(365-18)!}}{365^{18}}\] or

\[1 - \frac{\frac{365!}{347!}}{365^{18}}\]

In R there is a function called factorial() but factorials get large fast and we will overflow the memory. Try factorial(365) in R to see what happens.

It is returning infinity because the number is too large for the buffer. As is often the case we will have when using a computational method, we must be clever about our approach. Instead of using factorials we can make use of R s ability to work on vectors. If we provide R with a vector of values, the prod() will perform a product of all the elements.

7.4.5 General solution

We now have the mathematics to understand the problem. We can easily generalize this to any number of people. To do this, we have to write a function in R . As with everything in R , we save a function as an object. The general format for creating a function is

For this problem we will call the function birthday_prob() . The only parameter we need is the number of people in the room, n . Let’s write this function.

Notice we assigned the function to the name birthday_prob , we told R to expect one argument to the function, which we are calling n , and then we provide R with the code to find the probability. We set a default value for n in case one is not provided to prevent an error when the function is run. We will learn more about writing functions over this and the next semester.

Test the code with a know answer.

Now we can determine the probability for any size room. You may have heard that it only takes about 23 people in a room to have a 50% probability of at least 2 people matching birthdays.

Let’s create a plot of the probability versus number of people in the room. To do this, we need to apply the function to a vector of values. The function sapply() will work or we can also use Vectorize() to alter our existing function. We choose the latter option.

First notice what happens if we input a vector into our function.

It only uses the first value. There are several ways to solve this problem. We can use the map() function in the purrr package. This idea of mapping a function to a vector is important in data science. It is used in scenarios where there is a lot of data. In this case the idea of map-reduce is used to make the analysis amenable to parallel computing.

We could also just vectorize the function.

Now notice what happens.

We are good to go. Let’s create our line plot, Figure 7.2 .

Figure 7.2: The probability of at least 2 people having mathcing birthdays

Is this what you expected the curve to look like? We, the authors, did not expect this. It has a sigmodial shape with a large increase in the middle range and flatten in the tails.

7.4.6 Data science approach

The final approach we will take is one based on data, a data science approach. In the mosaicData package is a data set called Births that contains the number of births in the US from 1969 to 1988. This data will allow us to estimate the number of births on any day of the year. This allows us to eliminate the reliance on the assumption that each day is equally likely. Let’s first inspect() the data object.

It could be argued that we could randomly pick one year and use it. Let’s see what happens if we just used 1969. Figure 7.3 is a scatter plot of the number of births in 1969 for each day of the year.

Figure 7.3: The number of births for each day of the year in 1969

Exercise : What patterns do you see in Figure 7.3 ? What might explain them?

There are definitely bands appearing in the data which could be the day of the week; there are less birthdays on the weekend. There is also seasonality with more birthdays in the summer and fall. There is also probably an impact from holidays.

Quickly, let’s look at the impact of day of the week by using color for day of the week. Figure 7.4 makes it clear that the weekends have less number of births as compared to the work week.

Figure 7.4: The number of births for each day of the year in 1969 broken down by day of the week

By only using one year, this data might give poor results since holidays will fall on certain days of the week and the weekends will also be impacted. Note that we also still have the problem of leap years.

The years 1972, 1976, 1980, 1984, and 1988 are all leap years. At this point, to make the analysis easier, we will drop those years.

Notice in filter() we used the %in% argument. This is a logical argument checking if year is one of the values. The ! at the front negates this in a sense requiring year not to be one of those values.`

We are almost ready to simulate. We need to get the count of births on each day of the year for the non-leap years.

Let’s look at a plot of the number of births versus day of the year. We combined years in Figure 7.5 .

Figure 7.5: Number of births by day of the year for all years.

This curve has the seasonal cycling we would expect. The smaller scale cycling is unexpected. Maybe because we are dropping the leap years, we are getting some days appearing in our time interval more frequently on weekends. We leave it to you to investigate this phenomenon.

We use these counts as weights in a sampling process. Days with more births will have a higher probability of being selected. Days such as Christmas and Christmas Eve have a lower probability of being selected. Let’s save the weights in an object to use in the sample() function.

The pull() function pulls the vectors of values out of the data frame format into a vector format which the sample() needs.

Now let’s simulate the problem. The probability of a match should change slightly, maybe go down slightly?, but not much since most of the days have about the same probability or number of occurrences.

We could not solve this problem of varying frequency of birth days using mathematics, at least as far as we know.

Cool stuff, let’s get to learning more about probability models in the next chapters.

7.5 Homework Problems

• Exactly 2 people with the same birthday - Simulation . Complete a similar analysis for case where exactly 2 people in a room of 23 people have the same birthday. In this exercise you will use a computational simulation.
• Create a new R Markdown file and create a report. Yes, we know you could use this file but we want you to practice generating your own report.
• Simulate having 23 people in the class with each day of the year equally likely. Find the cases where exactly 2 people have the same birthday, you will have to alter the code from the Notes more than changing 18 to 23.
• Plot the frequency of occurrences as a bar chart.
• Estimate the probability of exactly two people having the same birthday.
• Exactly 2 people with the same birthday - Mathematical . Repeat problem 1 but do it mathematically. As a big hint, you will need to use the choose() function. The idea is that with 23 people we need to choose 2 of them to match. We thus need to multiply, the multiplication rule again, by choose(23,2) . If you are having trouble, work with a total of 3 people in the room first.
• Find a formula to determine the exact probability of exactly 2 people in a room of 23 having the same birthday.
• Generalize your solution to any number n people in the room and create a function.
• Vectorize the function.
• Plot the probability of exactly 2 people having the same birthday versus number of people in the room.
• Comment on the shape of the curve and explain it.

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CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

• Class 10th Science Case Study Questions
• Assertion and Reason Questions of Class 10th Science
• Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14  Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15  Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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CBSE Case Study Questions for Class 9 Maths Probability Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 9 Maths Probability  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 9 Maths Probability PDF

Checkout our case study questions for other chapters.

• Chapter 11 Constructions Case Study Questions
• Chapter 12 Heron’s Formula Case Study Questions
• Chapter 13 Surface Areas and Volumes Case Study Questions
• Chapter 14 Statistics Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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Case Study Questions for Class 9 Maths Chapter 15 Probability

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Here we are providing Case Study Questions for Class 9 Maths Chapter 15 Probability.

Case Study Questions

Question 1:

A jeweller has different types of bracelets in his shop. Sunita wants to purchase a bracelet for her sister’s birthday gift. When Sunita goes to shop, she founds the following data which represents the number of bracelets of different types in the shop.

(i) Find the probability that Sunita chooses Chain Bracelet. (a) 23/180 (b) 37/180 (c) 37/90 (d) 23/90

(ii) Find the probability that she chooses Pearl bracelet. (a) 23/180 (b) 37/180 (c) 37/90 (d) 23/90

(iii) What is the probability of a sure event? (a) 1 (b) 0 (c) 1/2 (d) 2/3

(iv) What is the probability that she chooses neither Bangle bracelet nor Pearl bracelet? (a) 23/180 (b) 45/180 (c) 109/180 (d) 23/45

(v) What is the probability that Sunita purchased a Cuff bracelet? (a) 6/17 (b) 2/13 (c) 1 (d) 2/15

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Class 11th Applied Mathematics - Probability Case Study Questions and Answers 2022 - 2023

Class 11th Applied Mathematics - Probability Case Study Questions and Answers 2022 - 2023 Study Materials Sep-09 , 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 11 Applied Mathematics Subject - Probability, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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Probability case study questions with answer key.

Final Semester - June 2015

(ii) Siddhartha draw four cards, find the probability that one of the four cards is an ace.

(iii) Ravi draw four cards, find the probability that one card is drawn from each suit.

(iv) Ravi again draw four card, find the probability that all the cards are of same colour.

(v) Siddhartha draws four cards successively without replacement. What is the probability that all the four cards are kings.

(ii) Rahul got next chance. What is the probability that he got the sum of the two number appearing on the top face of the dice is 13 ?

(iii) Now it was Ravi's turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12 ?

(iv) Rahul got next change. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal 7 ?

(v) Now it was Ravi's turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8

(ii) Rohini draw a card, what is the probability that the card drawn is an ace ?

(iii) Vijayata draw the card again, now what is the probability that the card drawn is a red card ?

(iv) Rohini draw the card again, now what is the probability that the card is an ace of red colour ?

(v) Now, Vijeta draw two cards successively with replacement, find the probability distribution of number of aces when one ace is there in selection.

(ii) What is the probability that Abhay and Rohit may hit but Varun may not hit

(iii) Probabilty that any two among Varun, Abhay and Rohit may hit the target is 

(iv) What is the probability that none of them will hit the target is

(v) When we find the probability then sum of all probabilities can be greater then one ? This statement is

*****************************************

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• Class 11 Maths
• Chapter 16: Probability

Important Questions for Class 11 Maths Chapter 16 - Probability

Important questions for class 11 Maths Chapter 16 Probability are given here, which are taken from the previous year’s question paper. Go through all the problems provided here, which will help you to score good marks in Class 11 final examination. Before solving the problems, be thorough with the concepts covered in the chapter – Probability. All the important questions in chapter 16 probability are solved here in a step-by-step procedure. Students can prepare these questions for the upcoming examinations because most of the questions are asked from the previous year’s question papers. Also, get important questions for class 11 Maths for all the chapters at BYJU’S.

Class 11 Maths Chapter 16 – Probability covers important concepts, such as random experiment, algebra of events, events and types of events, axiomatic approach to the probability

Also, check:

• Important 1 Mark Questions for CBSE Class 11 Maths
• Important 4 Marks Questions for CBSE Class 11 Maths
• Important 6 Marks Questions for CBSE Class 11 Maths

Important Questions for Class 11 Maths Chapter 16 Probability with Solutions

The most important questions for class 11 Maths Chapter 16 probability are provided with solutions. It includes MCQs, short type and long type answers. Practice these problems in a smart way a achieve good marks in the examination.

Question 1:

If P(A) is ⅗. Find P (not A)

Given that: P(A) = ⅗

To find P(not A) = 1 – P(A)

P (not A) = 1- ⅗

Therefore, P(not A) = ⅖.

Question 2:

Find the probability that when a hand of 7 cards are drawn from the well-shuffled deck of 52 cards, it contains

(i) all kings and (ii) 3 kings

(i) To find the probability that all the cards are kings:

If 7 cards are chosen from the pack of 52 cards

Then the total number of combinations possible is: 52 C 7

= 52!/ (7! 45!)

Assume that A be the event that all the kings are selected

We know that there are only 4 kings in the pack of 52 cards

Thus, if 7 cards are chosen, 4 kings are chosen out of 4, and 3 should be chosen from the 48 remaining cards.

Therefore, the total number of combinations is:

n(A) = 4 C 4 x 48 C 3

= 48!/3! 45!

Therefore, P(A) = n(A)/n(S)

Therefore, the probability of getting all the 7 cards are kings is 1/7735

(ii) To find the probability that 3 cards are kings:

Assume that B be the event that 3 kings are selected.

Thus, if 7 cards are chosen, 3 kings are chosen out of 4, and 4 cards should be chosen from the 48 remaining cards.

n(B) = 4 C 3 x 48 C 4

Therefore, P(B) = n(B)/n(S)

Therefore, the probability of getting 3 kings is 9/1547

Question 3:

An urn contains 6 balls of which two are red and four are black. Two balls

are drawn at random. The probability that they are of different colours is

(i)⅖ (ii)1/15 (iii)8/15 (iv)4/15

A correct answer is  an option (c)

Explanation:

Given that, the total number of balls = 6 balls

Let A and B be the red and black balls respectively,

The probability that two balls drawn, are different = P(the first ball drawn is red)(the second ball drawn is black)+ P(the first ball drawn is black)P(the second ball drawn is red)

= (2/6)(4/5) + (4/6)(2/5)

=(8/30)+ (8/30)

Question 4:

A couple has two children,

(i) Find the probability that both children are males if it is known that at least one of the children is male.

(ii) Find the probability that both children are females if it is known that the elder child is a female.

Let, the boy be denoted by b & girl be denoted by g

So, S = {(b, b) ,(b, g),(g, b), (g, g)}

To find probability that both children are males, if known that at least one of children is male

Let E : Both children are males F : At least one child is male

To find P(E|F)

E : Both children are males

E = {(b, b)}

F : At least one child is male

F = {(b, g), (g, b), (b, b)}

E ∩ F = {(b, b)}

P(E ∩ F ) = 1/4

P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹))

= (1/4)/(3/4)

∴ Required Probability is 𝟏/𝟑

S = {(b, b) ,(b, g),(g, b), (g, g)}

To find the probability that both children are females, if from that the elder child is a female.

Let E : both children are females F : elder child is a female

E : both children are females

E = {(g, g)}

F : elder child is a female

F = {(g, b), (g, g)}

P(F) = 2/4=1/2

Also, E ∩ F = {(g, g)}

So, P(E ∩ F) = 1/4

= (1/4)/(1/2)

Question 5:

One card is drawn from a well-shuffled pack of 52 cards. What is the probability that a card will be

(i) a diamond

(ii) Not an ace

(iii) a black card

(iv) not a diamond

(i) the probability that a card is a diamond

We know that there are 13 diamond cards in a deck. Therefore, the required probability is:

P( getting a diamond card) = 13/52 = ¼

(ii) the probability that a card is not an ace

We know that there are 4 ace cards in a deck.

Therefore, the required probability is:

P(not getting an ace card) = 1-( 4/52)

= 1- (1/13)

(iii) the probability that a card is a black card

We know that there are26 black cards in a deck.

P(getting a black card) = 26/52 = ½

(iv) the probability that a card is not a diamond

We know that there are 13 diamond cards in a deck.

We know that the probability of getting a diamond card is 1/4

P( not getting a diamond card) = 1- (1/4)

Question 6:

A pack of 50 tickets is numbered from 1 to 50 and is shuffled. Two tickets are drawn at random. Find the probability that (i) both the tickets drawn bear prime numbers (ii) Neither of the tickets drawn bear prime numbers.

The total number of tickets = 50

Prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

The total number of prime numbers between 1 and 50 is 15.

(i) Probability that both tickets are drawn bears prime numbers:

P(Both tickets bearing prime numbers ) = 15 C 2 / 50 C 2

Hence, the probability that both tickets are drawn bear prime numbers is 3/35.

(ii) Probability that neither of the tickets drawn bears prime numbers:

P ( Neither of the tickets bearing prime numbers) = 35 C 2 / 50 C 2

Therefore, the probability that neither of the tickets drawn bears a prime number is 17/35.

Question 7:

20 cards are numbered from 1 to 20. If one card is drawn at random, what is the probability that the number on the card is:

• Prime number
• A multiple of 5
• Not divisible by 3

Let S be the sample space.

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

(1) Probability that the card drawn is a prime number:

Let E 1 be the event of getting a prime number.

E 1 = {2, 3, 5, 7, 11, 13, 17, 19}

Hence, P(E 1 ) = 8/20 = 2/5.

(2) Probability that the card drawn is an odd number:

Let E 2 be the event of getting an odd number.

E 2 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

Hence, P(E 2 ) = 10/20 = 1/2.

(3) Probability that the card drawn is a multiple of 5

Let E 3 be the event of getting a multiple of 5

E 3 = {5, 10, 15, 20}

Hence, P(E 3 ) = 4/20 = 1/5.

(4) Probability that the card drawn is not divisible by 3:

Let E 4 be the event of getting a number that is not divisible by 3.

E 4 = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20}

Hence, P(E 4 ) = 14/20 = 7/10.

Important Questions for Class 11 Maths Chapter 16 Probability – Practice Questions

Practice the problems given below:

• What is the sample space for throwing a die?
• What is the sample space for tossing a coin?
• What is the sample space for the simultaneous toss of a die and a coin?
• In a single throw of two dice, find the probability of obtaining a total of 8.
• A bag contains 9 red and 12 white balls. One ball is drawn at random. Find the probability that the ball is drawn is red.
• What is the probability that the ordinary year has 53 Sundays?
• A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of its being a spade or a king.
• A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card?
• A number is chosen from the number 1 to 100. Find the probability of its being divisible by 4 or 6.
• Two cards are drawn at random from a pack of 52 cards. What is the probability that both the drawn cards are aces?
• A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
• A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of being either red or king.

To learn more important questions for class 11 Maths chapters, stay tuned with BYJU’S – The Learning App and download the app to learn all Maths-related concepts quickly by exploring more videos.

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• Class 11 Mathematics Case...

Class 11 Mathematics Case Study Questions

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If you’re seeking a comprehensive and dependable study resource with Class 11 mathematics case study questions for CBSE, myCBSEguide is the place to be. It has a wide range of study notes, case study questions, previous year question papers, and practice questions to help you ace your examinations. Furthermore, it is routinely updated to bring you up to speed with the newest CBSE syllabus. So, why delay? Begin your path to success with myCBSEguide now!

The rationale behind teaching Mathematics

The general rationale to teach Mathematics at the senior secondary level is to assist students:

• In knowledge acquisition and cognitive understanding of basic ideas, words, principles, symbols, and mastery of underlying processes and abilities, notably through motivation and visualization.
• To experience the flow of arguments while demonstrating a point or addressing an issue.
• To use the information and skills gained to address issues using several methods wherever possible.
• To cultivate a good mentality in order to think, evaluate, and explain coherently.
• To spark interest in the subject by taking part in relevant tournaments.
• To familiarise pupils with many areas of mathematics utilized in daily life.
• To pique students’ interest in studying mathematics as a discipline.

Case studies in Class 11 Mathematics

A case study in mathematics is a comprehensive examination of a specific mathematical topic or scenario. Case studies are frequently used to investigate the link between theory and practise, as well as the connections between different fields of mathematics. A case study will frequently focus on a specific topic or circumstance and will investigate it using a range of methodologies. These approaches may incorporate algebraic, geometric, and/or statistical analysis.

Sample Class 11 Mathematics case study questions

When it comes to preparing for Class 11 Mathematics, one of the best things Class 11 Mathematics students can do is to look at some Class 11 Mathematics sample case study questions. Class 11 Mathematics sample case study questions will give you a good idea of the types of Class 11 Mathematics sample case study questions that will be asked in the exam and help you to prepare more effectively.

Looking at sample questions is also a good way to identify any areas of weakness in your knowledge. If you find that you struggle with a particular topic, you can then focus your revision on that area.

myCBSEguide offers ample Class 11 Mathematics case study questions, so there is no excuse. With a little bit of preparation, Class 11 Mathematics students can boost their chances of getting the grade they deserve.

Some samples of Class 11 Mathematics case study questions are as follows:

Class 11 Mathematics case study question 1

• 9 km and 13 km
• 9.8 km and 13.8 km
• 9.5 km and 13.5 km
• 10 km and 14 km
• x  ≤   −1913
• x <  −1613
• −1613  < x <  −1913
• There are no solution.
• y  ≤   12 x+2
• y >  12 x+2
• y  ≥   12 x+2
• y <  12 x+2

Answer Key:

• (b) 9.8 km and 13.8 km
• (a) −1913   ≤  x 
• (b)  y >  12 x+2
• (d) (-5, 5)

Class 11 Mathematics case study question 2

• 2 C 1 × 13 C 10
• 2 C 1 × 10 C 13
• 1 C 2 × 13 C 10
• 2 C 10 × 13 C 10
• 6 C 2​ × 3 C 4   × 11 C 5 ​
• 6 C 2​ × 3 C 4   × 11 C 5
• 6 C 2​ × 3 C 5 × 11 C 4 ​
• 6 C 2 ​  ×   3 C 1 ​  × 11 C 5 ​
• (b) (13) 4  ways
• (c) 2860 ways.

Class 11 Mathematics case study question 3

Read the Case study given below and attempt any 4 sub parts: Father of Ashok is a builder, He planned a 12 story building in Gurgaon sector 5. For this, he bought a plot of 500 square yards at the rate of Rs 1000 /yard². The builder planned ground floor of 5 m height, first floor of 4.75 m and so on each floor is 0.25 m less than its previous floor.

Class 11 Mathematics case study question 4

Read the Case study given below and attempt any 4 sub parts: villages of Shanu and Arun’s are 50km apart and are situated on Delhi Agra highway as shown in the following picture. Another highway YY’ crosses Agra Delhi highway at O(0,0). A small local road PQ crosses both the highways at pints A and B such that OA=10 km and OB =12 km. Also, the villages of Barun and Jeetu are on the smaller high way YY’. Barun’s village B is 12km from O and that of Jeetu is 15 km from O.

Now answer the following questions:

• 5x + 6y = 60
• 6x + 5y = 60
• (a) (10, 0)
• (b) 6x + 5y = 60
• (b) 60/√ 61 km
• (d) 2√61 km

A peek at the Class 11 Mathematics curriculum

The Mathematics Syllabus has evolved over time in response to the subject’s expansion and developing societal requirements. The Senior Secondary stage serves as a springboard for students to pursue higher academic education in Mathematics or professional subjects such as Engineering, Physical and Biological Science, Commerce, or Computer Applications. The current updated curriculum has been prepared in compliance with the National Curriculum Framework 2005 and the instructions provided by the Focus Group on Teaching Mathematics 2005 in order to satisfy the rising demands of all student groups. Greater focus has been placed on the application of various principles by motivating the themes from real-life events and other subject areas.

Class 11 Mathematics (Code No. 041)

Design of Class 11 Mathematics exam paper

CBSE Class 11 mathematics question paper is designed to assess students’ understanding of the subject’s essential concepts. Class 11 mathematics question paper will assess their problem-solving and analytical abilities. Before beginning their test preparations, students in Class 11 maths should properly review the question paper format. This will assist Class 11 mathematics students in better understanding the paper and achieving optimum scores. Refer to the Class 11 Mathematics question paper design provided.

 Class 11 Mathematics Question Paper Design

• No chapter-wise weightage. Care to be taken to cover all the chapters.
• Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.  

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections.

  Prescribed Books:

• Mathematics Textbook for Class XI, NCERT Publications
• Mathematics Exemplar Problem for Class XI, Published by NCERT
• Mathematics Lab Manual class XI, published by NCERT

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