NCERT Solutions for Class 12 Maths Chapter 13 Probability
Thank you for reading this post, don't forget to subscribe!Exercise 13.1
Question 1:
Given that E and F are 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).
Question 2:
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
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)
Question 4:
Evaluate P(A ∪ B), if 2P(A) = P(B) = \(\frac{5}{13}\) and P(A|B) = \(\frac{2}{5}\) .
Question 5:
If P(A) = \(\frac{6}{11}\), P(B) = \(\frac{5}{11}\) and P(A ∪ B) = \(\frac{7}{11}\),
find (i) P(A∩B) (ii) P(A|B) (iii) P(B|A)
Determine P(E|F) in Exercises 6 to 9.
Question 6:
A coin is tossed three times, where
(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
Question 7:
Two coins are tossed once, where
(i) E : tail appears on one coin, F : one coin shows head
(ii) E : no tail appears, F : no head appears
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
Question 9:
Mother, father and son line up at random for a family picture
E : son on one end, F : father in middle
Question 10:
A black and a red dice 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.
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)
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, (ii) 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?
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’.
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’.
In each of the Exercises 16 and 17 choose the correct answer:
Question 16:
If P(A) = \(\frac{1}{2}\), P(B) = 0, then P(A|B) is
(A) 0 (B) \(\frac{1}{2}\) (C) not defined (D) 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)
NCERT Solutions for Class 12 Maths Chapter 13 Probability
Exercise 13.2
Question 1:
If P(A) = \(\frac{3}{5}\) and P (B) = \(\frac{1}{5}\) , find P (A ∩ B) if A and B are independent events.
Question 2:
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
Question 3:
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.
Question 4:
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
Question 5:
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even,’ and B be the event, ‘the number is red’. Are A and B independent?
Question 6:
Let E and F be events with P(E) = \(\frac{3}{5}\), P(F) = \(\frac{3}{10}\) and P (E ∩ F) = \(\frac{1}{5}\). Are
E and F independent?
Question 7:
Given that the events A and B are such that P(A) = \(\frac{1}{2}\), P(A ∪ B) = \(\frac{3}{5}\) and P(B) = p. Find p if they are (i) mutually exclusive (ii) independent.
Question 8:
Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find
(i) P(A ∩ B) (ii) P(A ∪ B) (iii) P (A|B) (iv) P (B|A)
Question 9:
If A and B are two events such that P(A) = \(\frac{1}{4}\), P (B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{8}\), find P (not A and not B).
Question 10:
Events A and B are such that P (A) = \(\frac{1}{2}\) , P(B) = \(\frac{7}{12}\) and P(not A or not B) = \(\frac{1}{4}\). State whether A and B are independent ?
Question 11:
Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6.
Find
(i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)
Question 12:
A die is tossed thrice. Find the probability of getting an odd number at least once.
Question 13:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
(i) both balls are red.
(ii) first ball is black and second is red.
(iii) one of them is black and other is red.
Question 14:
Probability of solving specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\)respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved (ii) exactly one of them solves the problem.
Question 15:
One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent ?
(i) E : ‘the card drawn is a spade’
F : ‘the card drawn is an ace’
(ii) E : ‘the card drawn is black’
F : ‘the card drawn is a king’
(iii) E : ‘the card drawn is a king or queen’
F : ‘the card drawn is a queen or jack’
Question 16:
In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.
(a) Find the probability that she reads neither Hindi nor English newspapers.
(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.
(c) If she reads English newspaper, find the probability that she reads Hindi newspaper.
Choose the correct answer in Exercises 17 and 18.
Question 17:
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
(A) 0 (B) \(\frac{1}{3}\) (C) \(\frac{1}{12}\) (D) \(\frac{1}{36}\)
Question 18:
Two events A and B will be independent, if
(A) A and B are mutually exclusive
(B) P(A′B′) = [1 – P(A)] [1 – P(B)]
(C) P(A) = P(B)
(D) P(A) + P(B) = 1
