# NCERT Solutions for Miscellaneous Exercise Chapter 13 Class 12 - Probability

NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise consist of different types of questions covering all the concepts of probability Class 12 Maths NCERT syllabus. These questions can be practised, if you have solved all the previous NCERT book chapter 13 exercises. Miscellaneous exercise chapter 13 Class 13 questions are a bit difficult than all the previous exercises questions. You are advised to solve all exercise questions by yourself. If you find difficulties while solving them, you can go through NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise. There are very few questions asked in the board exams from miscellaneous exercises, it is not considered to be very important for board exams. You can solve these exercises to be on the safer side in the board exams. These exercises are very important for competitive exams, so you must solve them as well. You can also check for NCERT Solutions.

**Also, see**

- Probability Exercise 13.1
- Probability Exercise 13.2
- Probability Exercise 13.3
- Probability Exercise 13.4
- Probability Exercise 13.5

**Probability Class 12 Chapter 13****-Miscellaneous Exercise**

**Question:1(i)** A and B are two events such that Find if

is a subset of

**Answer:**

A and B are two events such that

**Question:2(i)** A couple has two children,

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

**Answer:**

A couple has two children,

sample space

Let A be both children are males and B is at least one of the children is male.

**Question:2(ii) **A couple has two children,

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

**Answer:**

A couple has two children,

sample space

Let A be both children are females and B be the elder child is a female.

**Answer:**

We have of men and of women have grey hair.

Percentage of people with grey hairs

The probability that the selected haired person is male :

**Answer:**

of people are right-handed.

at most of a random sample of people are right-handed.

the probability that more than of a random sample of people are right-handed is given by,

the probability that at most of a random sample of people are right-handed is given by

.

all will bear mark.

**Answer:**

Total balls in urn = 25

Balls bearing mark 'X' =10

Balls bearing mark 'Y' =15

balls are drawn with replacement.

Let Z be a random variable that represents a number of balls with Y mark on them in the trial.

Z has a binomial distribution with n=6.

not more than will bear mark.

**Answer:**

Total balls in urn = 25

Balls bearing mark 'X' =10

Balls bearing mark 'Y' =15

balls are drawn with replacement.

Let Z be random variable that represents number of balls with Y mark on them in trial.

Z has binomail distribution with n=6.

the number of balls with mark and mark will be equal.

**Answer:**

**Answer:**

Let p and q respectively be probability that the player will clear and knock down the hurdle.

Let X represent random variable that represent number of times the player will knock down the hurdle.

**Answer:**

Probability of 6 in a throw of die =P

Probability that 2 sixes come in first five throw of die :

Probability that third six comes in sixth throw :

**Question:8** If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?

**Answer:**

In a leap year, there are 366 days.

In 52 weeks, there are 52 Tuesdays.

The probability that a leap year will have 53 Tuesday is equal to the probability that the remaining 2 days are Tuesday.

The remaining 2 days can be :

1. Monday and Tuesday

2. Tuesday and Wednesday

3. Wednesday and Thursday

4. Thursday and Friday

5.friday and Saturday

6.saturday and Sunday

7.sunday and Monday

Total cases = 7.

Favorable cases = 2

Probability of having 53 Tuesday in a leap year = P.

**Answer:**

Probability of success is twice the probability of failure.

Let probability of failure be X

then Probability of success = 2X

Sum of probabilities is 1.

Let and

Let X be random variable that represent the number of success in six trials.

**Answer:**

Let the man toss coin n times.

Probability of getting head in first toss = P

The minimum value to satisfy the equation is 4.

The man should toss a coin 4 or more times.

**Answer:**

In a throw of die,

probability of getting six = P

probability of not getting six = q

There are three cases :

1. Gets six in the first throw, required probability is

The amount he will receive is Re. 1

2.. Does not gets six in the first throw and gets six in the second throw, then the probability

The amount he will receive is - Re.1+ Re.1=0

3. Does not gets six in first 2 throws and gets six in the third throw, then the probability

Amount he will receive is -Re.1 - Re.1+ Re.1= -1

Expected value he can win :

**Question:12(i)** Suppose we have four boxes A,B,C and D containing coloured marbles as given below:

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A ?

**Answer:**

'

Let R be the event of drawing red marble.

Let respectively denote the event of selecting box A, B, C.

Total marbles = 40

Red marbles =15

Probability of drawing red marble from box A is

**Question:12(ii)** Suppose we have four boxes A,B,C and D containing coloured marbles as given below:

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box B?

**Answer:**

Let R be event of drawing red marble.

Let respectivly denote event of selecting box A,B,C.

Total marbles = 40

Red marbles =15

Probability of drawing red marble from box B is

**Question:12(iii)** Suppose we have four boxes A,B,C and D containing coloured marbles as given below:

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box C?

**Answer:**

Let R be event of drawing red marble.

Let respectivly denote event of selecting box A,B,C.

Total marbles = 40

Red marbles =15

Probability of drawing red marble from box C is

**Answer:**

Let A,E1, E2 respectively denote the event that a person has a heart break, selected person followed the course of yoga and meditation , and the person adopted

the drug prescription.

the probability that the patient followed a course of meditation and yoga is

**Answer:**

Total number of determinant of second order with each element being 0 or 1 is

The values of determinant is positive in the following cases

Probability is

P(A fails) =

P(B fails alone) =

P(A and B fail) =

Evaluate the following probabilities

**Answer:**

Let event in which A fails and B fails be

P(A fails) =

P(B fails alone) =

P(A and B fail) =

Evaluate the following probabilities

**Answer:**

Let event in which A fails and B fails be

**Answer:**

Let E1 and E2 respectively denote the event that red ball is transfered from bag 1 to bag 2 and a black ball is transfered from bag 1 to bag2.

and

Let A be the event that ball drawn is red.

When a red ball is transfered from bag 1 to bag 2.

When a black ball is transfered from bag 1 to bag 2.

**Question:17 **If A and B are two events such that and then

Choose the correct answer of the following:

(A)

(B)

(C)

(D)

**Answer:**

A and B are two events such that and

Option A is correct.

**More About ****NCERT Solutions for Class 12 Maths Chapter 13 Miscellaneous Exercise:-**

As the name suggests NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise consist of different types of questions from all the previous exercises of the probability. This exercise is considered to be tough as compared to the previous exercises but it is not as important as previous exercises of this chapter for board exams. There are very few questions in board exams that are asked from miscellaneous exercises but it is very important for competitive exams. Students are advised to solve this exercise also to get command on the concept.

**Benefits of NCERT Solutions for Class 12 Maths Chapter 13 Miscellaneous Exercise:-**

- NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise
- There are 19 questions and 5 examples given in the miscellaneous exercise which you can solve to get a command on the probability theory.
- NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise
- Miscellaneous exercise chapter 13 Class 12
- NCERT solutions for Class 12 Maths chapter 13 miscellaneous Exercise

**Also see-**

**NCERT Solutions of Class 12 Subject Wise**

**Subject Wise NCERT Exampler Solutions**

**Happy learning!!!**

## Frequently Asked Question (FAQs) - NCERT Solutions for Miscellaneous Exercise Chapter 13 Class 12 - Probability

**Question: **Do questions from the miscellaneous exercises comes in 12th board exams?

**Answer: **

More than 95% of questions in the board's exam are not asked from miscellaneous exercises but it is very important for competitive exams.

**Question: **What are the topics in miscellaneous exercise probability Class 12 ?

**Answer: **

Miscellaneous exercise is consists of different questions from all the topics of probability Class 12 Maths.

**Question: **What is the probability of an impossible event ?

**Answer: **

The probability of an impossible event is 0.

**Question: **What is the probability of getting 0 when we roll a die ?

**Answer: **

The probability of getting 0 when we roll a die is zero.

**Question: **What is the probability of getting number less than 7 when we roll a die ?

**Answer: **

The probability of a number less than 7 when we roll a die is one.

**Question: **Give an example of certain event .

**Answer: **

The event of getting a number less than 7 when we roll a die is an example of a certain event.

**Question: **Give an example of impossible event ?

**Answer: **

The event of getting number 0 we roll a die is an example of an impossible event.

**Question: **Where can I get NCERT solutions ?

**Answer: **

Here you can get NCERT Solutions.

## Latest Articles

##### Manipur Board 12th Time Table 2023 - Check Class 12 Exam Date ...

Manipur Board 12th Time Table 2023- COHSEM will release the cl...

##### CG Open School Time Table 2023 for Class 10th & 12th

CG Open School Time Table 2023 - CGSOS will release the CG ope...

##### The Lexicon Schools Organise LEXIMUN’ 2022

The Lexicon Schools, Pune, host the Lexicon Peace Summit, also...

##### NCERT Exemplar Class 11 Physics Solutions - Chapter Wise Probl...

NCERT Exemplar class 11 Physics solutions solved by subject ma...

##### NCERT Exemplar Class 11 Maths Solutions - Chapter Wise Problem...

NCERT Exemplar class 11 Maths solutions solved by subject matt...

##### Odisha CHSE Result 2022 (Declared) - Odisha Board 12th Result ...

Odisha CHSE Result 2022 - CHSE, Odisha has declared the Odisha...

##### Odisha CHSE Arts Result 2022 (Declared) - Check Odisha 12th Ar...

Odisha CHSE 12th Arts Result 2022 - Odisha Board has announced...

##### CGBSE 12th Time Table 2023 for Arts, Commerce & Science - Chec...

CGBSE 12th Time Table 2022 - Chhattisgarh Board of Secondary E...

##### Odisha CHSE Science Result 2022 (Declared) - Check result @ori...

Odisha CHSE Science Result 2022 - CHSE, Odisha has declared th...

##### Odisha CHSE Questions Papers 2022 – Download Previous Year Que...

Odisha CHSE Questions Papers 2022 – Odisha Board has provided ...