NCERT Solutions for Maths Class 12 Exercise 13.1

NCERT Solutions for Maths Class 12 Exercise 13.1

 

NCERT Solutions for Maths Class 12 Exercise 13.1


Hello Students. Welcome to maths-formula.com. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 13.1.

 

You can download the PDF of NCERT Books Maths Chapter 10 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 13.1.

 

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.

 

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.


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(AB), 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(AB) = 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.

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