**NCERT Solutions for Maths Class 12 Exercise 13.1**

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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

**NCERT Solutions for Maths Class 12 Exercise 13.1** helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from **NCERT Syllabus for Mathematics Class 12**.

**NCERT Solutions for Maths Class 12 Exercise 13.1** are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

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**NCERT Solutions for Maths Class 12 Exercise 13.2**

**NCERT Solutions for Maths Class 12 Exercise 13.3**

**NCERT Solutions for Maths Class 12 Exercise 13.4**

**NCERT Solutions for Maths Class 12 Exercise 13.5**

**NCERT Solutions for Maths Class
12 Exercise 13.1**

**Maths Class
12 Ex 13.1 Question 1. **

Given that E and
Fare events such that P(E) = 0.6, P(F) = 0.3 and P(E∩F) = 0.2,

find P(E|F) and P(F|E).

**Solution:**

Given that: P (E)
= 0.6, P (F) = 0.3, P (E∩F) = 0.2

**Maths Class
12 Ex 13.1 Question 2. **

Compute P(A|B), if
P(B) = 0.5 and P(A∩B) = 0.32.

**Solution:**

Given that: P (B)
= 0.5, P (A∩B) = 0.32

**Maths Class
12 Ex 13.1 Question 3. **

If P(A) = 0.8, P(B)
= 0.5 and P(B|A) = 0.4, find

(i) P(A∩B)

(ii) P(A|B)

(iii) P(A∪B)

**Solution:**

**Maths Class
12 Ex 13.1 Question 4.**

Evaluate P(A∪B), if 2P(A) = P(B) = 5/13 and
P(A|B) = 2/5.

**Solution:**

**Maths Class
12 Ex 13.1 Question 5.**

If P(A) = 6/11,
P(B) = 5/11 and P(A∪B) = 7/11, find

(i) P(A∩B)

(ii) P(A|B)

(iii) P(B|A)

**Solution:**

**Maths Class
12 Ex 13.1 Question 6.**

Determine P(E|F):
A coin is tossed three times.

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

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

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

**Solution:**

**Maths Class
12 Ex 13.1 Question 7.**

Determine P(E|F):
Two coins are tossed once.

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

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

**Solution:**

**Maths Class
12 Ex 13.1 Question 8.**

Determine P(E|F):
A die is thrown three times.

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

**Solution:**

A die is thrown
three times,

E: 4 appears on
third toss = {(1, 1, 4), (1, 2, 4), (1, 3, 4), (1, 4, 4), (1, 5, 4), (1, 6, 4),
(2, 1, 4), (2, 2, 4), (2, 3, 4), (2, 4, 4), (2, 5, 4), (2, 6, 4), (3, 1, 4), (3, 2, 4), (3, 3, 4), (3, 4, 4), (3, 5, 4),
(3, 6, 4), (4, 1, 4), (4, 2, 4), (4, 3, 4), (4, 4, 4), (4, 5, 4), (4, 6, 4), (5,
1, 4), (5, 2, 4), (5, 3, 4), (5, 4, 4), (5, 5, 4), (5, 6, 4), (6, 1, 4), (6, 2,
4), (6, 3, 4), (6, 4, 4), (6, 5, 4), (6, 6, 4)}

These are 36 cases.

F: 6 and 5
appears respectively on first two tosses

= {(6, 5, 1), (6,
5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6)}

These are six
cases. E ∩ F = {6, 5, 4}

**Maths Class
12 Ex 13.1 Question 9. **

Determine P(E|F):
Mother, father and son line up at random for a family picture.

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

**Solution:**

**Maths Class
12 Ex 13.1 Question 10.**

A black and a red
die are rolled.

(a) Find the conditional probability of obtaining a sum greater than 9, given
that the black die resulted in a 5.

(b) Find the conditional probability of obtaining the sum 8, given that the red
die resulted in a number less than 4.

**Solution:**

**Maths Class
12 Ex 13.1 Question 11.**

A fair die is
rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find

(i) P(E|F) and P(F|E)

(ii) P(E|G) and P(G|E)

(iii) P[(E∪F)|G] and P[(E∩F)|G]

**Solution:**

**Maths Class
12 Ex 13.1 Question 12.**

Assume that each
child born 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,

(ii) at least one is girl?

**Solution:**

Let first and
second girls are denoted by G_{1} and G_{2} and boys by B_{1}
and B_{2}.

Sample space, S = {(G_{1}G_{2}), (G_{1}B_{2}), (G_{2}B_{1}),
(B_{1}B_{2})}

Let A = Both the children are girls = {G_{1}G_{2}}

B = youngest child is a girl = {G_{1}G_{2}, B_{1}G_{2}}

C = at least one is a girl = {G_{1}B_{2}, G_{1}G_{2},
B_{1}G_{2}}

A∩B = {G_{1}G_{2}},

A∩C = {G_{1}G_{2}}

**Maths Class
12 Ex 13.1 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?

**Solution:**

The given data
may be tabulated as

**Maths Class
12 Ex 13.1 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’.

**Solution:**

**Maths Class
12 Ex 13.1 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’.

**Solution:**

**In each of the following, choose the correct
answer:**

**Maths Class
12 Ex 13.1 Question 16. **

If P(A) = 1/2,
P(B) = 0, then P(A|B) is

(A) 0

(B) ½

(C) not defined

(D) 1

**Solution:**

Given: P(A) = ½ and
P(B) = 0

∴ P(A∩B) = 0

∴ P(A|B) = P(A∩B)/P(B) = 0/0 = not defined

Hence, option (C) is correct.

**Maths Class
12 Ex 13.1 Question 17. **

If A and B are
events such that P(A|B) = P(B|A), then

(A) A⊂B but A ≠ B

(B) A = B

(C) A∩B = Ï†

(D) P(A) = P(B)

**Solution:**

P(A|B) = P(B|A)

P(A∩B)/P(B) = P(A∩B)/P(A)

⇒ P(A) = P(B)

Hence,
option (D) is correct.