Let A and B are two independent events such that $P(A) =\frac{3}{5}$ and $P(B)=\frac{4}{9}$.
Match List-I with List-II
|
List-I |
List-II |
|
(A) $P(A∩B)$ |
(I) $\frac{2}{5}$ |
|
(B) $P(A|B)$ |
(II) $\frac{4}{15}$ |
|
(C) $P(A'|B)$ |
(III) $\frac{3}{5}$ |
|
(D) $P(A'∩B')$ |
(IV) $\frac{2}{9}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
(A) $P(A∩B)=P(A)×P(B)$ [A and B are independent]
$=\frac{3}{5}×\frac{4}{9}=\frac{12}{45}=\frac{4}{15}$
(B) $P(A|B)=\frac{P(A∩B)}{P(B)}=\frac{\frac{4}{15}}{\frac{4}{9}}=\frac{3}{5}$
(C) $P(A'|B)=\frac{P(A'∩B)}{P(B)}=\frac{\frac{2}{5}×\frac{4}{9}}{\frac{4}{9}}=\frac{2}{5}$
(D) $P(A'∩B')=P(A')P(B')$
$=\frac{2}{5}×\frac{5}{9}=\frac{2}{9}$ [A' and B' are also independent events]