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 G1 and G2 and boys by B1
and B2.
Sample space, S = {(G1G2), (G1B2), (G2B1),
(B1B2)}
Let A = Both the children are girls = {G1G2}
B = youngest child is a girl = {G1G2, B1G2}
C = at least one is a girl = {G1B2, G1G2,
B1G2}
A∩B = {G1G2},
A∩C = {G1G2}
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 = φ
(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