# NCERT Solutions for Exercise 13.1 Class 12 Maths Chapter 13 - Probability

NCERT solutions for exercise 13.1 Class 12 Maths chapter 13 is very important for the students who wish to perform well in the 12th board exam. NCERT book exercise has covered topics like the probability of events, conditional probability, properties of conditional property, etc. Probability has a lot of real-life applications like forecasting the weather, sports, online gaming, insurance, politics lottery tickets, playing cards, statistics, etc. There area total of 17 questions covered in the exercise 13.1 Class 12 Maths which are mostly related to conditional probability. You are advised to solve all these NCERT syllabus problems on your own. You can go through NCERT solutions for Class 12 Maths chapter 13 exercise 13.1 If you are facing difficulties while solving these problems.

**Also, see**

- Probability Exercise 13.2
- Probability Exercise 13.3
- Probability Exercise 13.4
- Probability Exercise 13.5
- Probability Miscellaneous Exercise

**Probability Class 12 Chapter 13****-Exercise: 13.1 **

**Question:1**

Given that and are events such that and find and

** Answer: **

It is given that and

** Question:2 ** Compute if and

** Answer: **

It is given that and

** Question:3 ** If and find

(i)

** Answer: **

It is given that P(A)=0.8, P(B)=0.5 and P(B|A)=0.4

** Question:3 ** If and find

(ii)

** Answer: **

It is given that and

** Question:3 ** If and find

(iii)

** Answer: **

It is given that

** Question:4 ** Evaluate if and

** Answer: **

Given in the question and

We know that:

Use,

** Question:5 ** If and , find

(i)

** Answer: **

Given in the question

and

By using formula:

** Question:5 ** If and find

(ii)

** Answer: **

It is given that -

We know that:

** Question:5 ** If and find

(iii)

** Answer: **

Given in the question-

and

Use formula

** Question:6 ** A coin is tossed three times, where

(i)E : head on third toss ,F : heads on first two tosses

** Answer: **

The sample space S when a coin is tossed three times is

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

It can be seen that the sample space (S) has 8 elements.

Total number of outcomes

According to question

E: head on third toss, F: heads on first two tosses

** Question:6 ** A coin is tossed three times, where

(ii)E : at least two heads ,F : at most two heads

** Answer: **

The sample space S when a coin is tossed three times is

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

It can be seen that the sample space (S) has 8 elements.

Total number of outcomes

According to question

E : at least two heads , F : at most two heads

** Question:6 ** A coin is tossed three times, where

(iii)E : at most two tails ,F : at least one tail

** Answer: **

The sample space S when a coin is tossed three times is

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

It can be seen that the sample space (S) has 8 elements.

Total number of outcomes

According to question

E: at most two tails, F: at least one tail

** Question:7 ** Two coins are tossed once, where

(i) E : tail appears on one coin, F : one coin shows head

** Answer: **

E : tail appears on one coin, F : one coin shows head

Total outcomes =4

** Question:7 ** Two coins are tossed once, where

(ii)E : no tail appears,F : no head appears

** Answer: **

E : no tail appears, F : no head appears

Total outcomes =4

** Question:8 ** A die is thrown three times,

E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

** Answer: **

E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

Total outcomes

** Question:9 ** Mother, father and son line up at random for a family picture

E : son on one end, F : father in middle

** Answer: **

E : son on one end, F : father in middle

Total outcomes

Let S be son, M be mother and F be father.

Then we have,

** Question:10 ** A black and a red dice are rolled.

(a) Find the conditional probability of obtaining a sum greater than , given that the black die resulted in a

** Answer: **

A black and a red dice are rolled.

Total outcomes

Let the A be event obtaining a sum greater than and B be a event that the black die resulted in a

** Question:10 ** A black and a red dice are rolled.

(b) Find the conditional probability of obtaining the sum , given that the red die resulted in a number less than .

** Answer: **

A black and a red dice are rolled.

Total outcomes

Let the A be event obtaining a sum 8 and B be a event thatthat the red die resulted in a number less than .

Red dice is rolled after black dice.

** Question:11 ** A fair die is rolled. Consider events and Find

(i) and

** Answer: **

A fair die is rolled.

Total oucomes

and

** Question:11 ** A fair die is rolled. Consider events and Find

(ii) and

** Answer: **

A fair die is rolled.

Total oucomes

,

** Question:11 ** A fair die is rolled. Consider events and Find

(iii) and

** Answer: **

A fair die is rolled.

Total oucomes

and

,

** Question:12 ** Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that

(i) the youngest is a girl,

** Answer: **

Assume that each born child is equally likely to be a boy or a girl.

Let first and second girl are denoted by respectively also first and second boy are denoted by

If a family has two children, then total outcomes

Let A= both are girls

and B= the youngest is a girl =

Therefore, the required probability is 1/2

** Question:12 ** ** ** Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that

(ii) at least one is a girl?

** Answer: **

Assume that each born child is equally likely to be a boy or a girl.

Let first and second girl are denoted by respectively also first and second boy are denoted by

If a family has two children, then total outcomes

Let A= both are girls

and C= at least one is a girl =

** Question:13 ** An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

** Answer: **

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions.

Total number of questions

Let A = question be easy.

Let B = multiple choice question

easy multiple questions

Therefore, the required probability is 5/9

** Question:14 ** Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

** Answer: **

Two dice are thrown.

Total outcomes

Let A be the event ‘the sum of numbers on the dice is 4.

Let B be the event that two numbers appearing on throwing two dice are different.

Therefore, the required probability is 1/15

** Question:15 ** Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.

** Answer: **

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin.

Total outcomes

Total number of outcomes =20

Let A be a event when coin shows a tail.

Let B be a event that ‘at least one die shows a 3’.

** Question:16 ** In the following Exercise 16 choose the correct answer:

If then is

(A)

(B)

(C)

(D)

** Answer: **

It is given that

Hence, is not defined .

Thus, correct option is C.

** Question:17 ** In the following Exercise 17 choose the correct answer:

If and are events such that then

(A) but

(B)

(C)

(D)

** Answer: **

It is given that

Hence, option D is correct.

**More About ****NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.1:-**

Exercise 13.1 Class 12 Maths solutions** **are consist of questions related to conditional probability and different properties of conditional probability. There are 15 short answer type questions and 2 multiple choice types questions are given in this exercise. There are 7 solved examples given in the NCERT textbook before this exercise that is related to conditional probability. You can solve these examples before solving exercise problems, so it will be easy for you to solve exercise problems.

**Also Read| **Probability Class 12th Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.1:-**

- Class 12th Maths chapter 13 exercise 13.1 solutions are helpful for the students to get conceptual clarity about conditional probability and its applications.
- These exercise 13.1 Class 12 Maths solutions are designed by the subject matter experts who know how best to write the answer in the board exams in order to get good marks.
- These Class 12 Maths chapter 13 exercise 13.1 solutions could be be used for revision before the exam.
- These are some examples given in the Class 12 NCERT book before exercise 13.1 which could be solved before solving exercise 13.1.
- As most of the questions in the 12th board exams are directly asked from NCERT textbooks, you are advised to be thorough with the NCERT textbook.

**Also see-**

NCERT Solutions for Class 12 Maths Chapter 13

NCERT Exemplar Solutions Class 12 Maths Chapter 13

**NCERT Solutions of Class 12 Subject Wise**

NCERT Solutions for Class 12 Maths

NCERT Solutions for Class 12 Physics

NCERT Solutions for Class 12 Chemistry

NCERT Solutions for Class 12 Biology

**Subject Wise NCERT Exampler Solutions**

NCERT Exemplar Solutions for Class 12 Maths

NCERT Exemplar Solutions for Class 12 Physics

NCERT Exemplar Solutions for Class 12 Chemistry

NCERT Exemplar Solutions for Class 12 Biology

**Happy learning!!!**