Match List-I with List-II. Given $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{5}$ where A and B are independent.
| List-I | List-II | ||
| (A) | P(A ∩ B) | (I) | $\frac{7}{15}$ |
| (B) | P(A' ∩ B') | (II) | $\frac{2}{5}$ |
| (C) | P(at least one of the two events takes place) | (III) | $\frac{1}{15}$ |
| (D) | P(only one vent takes place) | (IV) | $\frac{8}{15}$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A) $P(A∩B)=P(A)P(B)=\frac{1}{15}$ (III)
(B) $P(\overline A∩\overline B)=P(\overline A)P(\overline B)=\frac{8}{15}$ (IV)
(C) P(atleast one) = $P(A∪B)=P(A)+P(B)-P(A∩B)=\frac{7}{15}$ (I)
(D) P(only one) = $P(A∪B)-P(A∩B)=\frac{2}{5}$ (II)