JEE Main 2020 · 8 January · evening · Single correct · +4 / −1
Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2 , then the probability of both of them occur together is :
- (a) 0.20
- (b) 0.02
- (c) 0.01
- (d) 0.10
Answer and solution
Answer (d) 0.10
Solution
Maths sir · 3 steps
Split A or B into two non-overlapping parts: exactly one happens, or both happen.
- Split the union. If A or B occurs, then either exactly one of them occurs or both occur. These two cases cannot happen together, so their probabilities just add.
P(A ∪ B) = P(exactly one) + P(A ∩ B)
- Put in numbers. 1/2 = 2/5 + P(A ∩ B), so P(A ∩ B) = 1/2 - 2/5 = (5 - 4)/10 = 1/10.
- So. The probability that both occur together is 1/10 = 0.10, which is option (d).
The idea to keep. Break "at least one" into "exactly one" plus "both". The two parts never overlap, so any one of the three probabilities follows from the other two by adding or subtracting.
Answer from the NTA final answer key. Solution by PrepWiser.