A and B are independent events with P(A) = 0.2 and P(B) = 0.6.
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Probability that both A and B occur | (I) | 0.56 |
| (B) | Probability that at least one of A and B occurs | (II) | 0.12 |
| (C) | Probability that exactly one of A and B occurs | (III) | 0.32 |
| (D) | Probability that neither A nor B occurs | (IV) | 0.68 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
For independent events, the probability that both happen is the product, and the complements are independent too. Here
\(P(A') = 0.8,\quad P(B') = 0.4\)
(A) Probability that both A and B occur
This matches (II) 0.12.
\(P(A\cap B) = 0.2\times 0.6 = 0.12\)
(B) Probability that at least one of A and B occurs
This matches (IV) 0.68.
\(P(A\cup B) = 0.2+0.6-0.12 = 0.68\)
(C) Probability that exactly one of A and B occurs
This matches (I) 0.56.
\(P(A\cap B') = 0.2\times 0.4 = 0.08\)
\(P(A'\cap B) = 0.8\times 0.6 = 0.48\)
\(P(\text{exactly one}) = 0.08+0.48 = 0.56\)
(D) Probability that neither A nor B occurs
This matches (III) 0.32.
\(P(A'\cap B') = 0.8\times 0.4 = 0.32\)