Hello Students. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 13.1**.

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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 13.1**

**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.

**Related Links:**

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