NCERT Class 12 Maths
Chapter 13: Probability
18 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 13 Probability — Exercise 13.2
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
If independent A,B have P(A)=3/5,P(B)=1/5, find P(A∩B).
Question 2
Draw two cards without replacement from 52. Find the probability both are black.
Question 3
Inspect three uniformly drawn oranges without replacement from 15, of which 12 are good. Approve only if all three are good. Find…
Question 4
A fair coin and unbiased die are tossed. Are A=head and B=die shows 3 independent?
Question 5
A die has 1,2,3 red and 4,5,6 green. Are A=even and B=red independent?
Question 6
P(E)=3/5,P(F)=3/10,P(E∩F)=1/5. Are E,F independent?
Question 7
P(A)=1/2,P(A∪B)=3/5,P(B)=p. Find p if (i) mutually exclusive, (ii) independent.
Question 8
Independent A,B have P(A)=0.3,P(B)=0.4. Find (i) intersection, (ii) union, (iii) P(A|B), (iv) P(B|A).
Question 9
P(A)=1/4,P(B)=1/2,P(A∩B)=1/8. Find P(A′∩B′).
Question 10
P(A)=1/2,P(B)=7/12,P(A′∪B′)=1/4. State whether A,B are independent.
Question 11
Independent A,B have P(A)=0.3,P(B)=0.6. Find (i) both, (ii) A and not B, (iii) at least one, (iv) neither.
Question 12
A fair die is tossed thrice. Find P(an odd number appears at least once).
Question 13
Two draws with replacement from 10 black and 8 red balls. Find (i) both red, (ii) first black then red, (iii) one of each.
Question 14
A,B solve a problem independently with probabilities 1/2,1/3. Find (i) P(problem solved), (ii) P(exactly one solves).
Question 15
For one random card, check independence: (i) spade vs ace; (ii) black vs king; (iii) king-or-queen vs queen-or-jack.
Question 16
A hostel has 60% Hindi-newspaper readers, 40% English, 20% both. Find (a) neither, (b) P(English|Hindi), (c) P(Hindi|English).
Question 17
Find the probability of an even prime number on each of two fair dice.
Question 18
Which condition guarantees independence of A,B?