Let A and B be two events such that $P(A) = 0.2, P(B) = 0.4, P(B|A) = 0.5$
|
List-I |
List-II |
|
(A) $P(A ∩ B)$ |
(I) 0.5 |
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(B) $P(A|B)$ |
(II) 0.8 |
|
(C) $P(A ∪ B)$ |
(III) 0.25 |
|
(D) $P(A')$ |
(IV) 0.1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
|
List-I |
List-II |
|
(A) $P(A ∩ B)$ |
(IV) 0.1 |
|
(B) $P(A|B)$ |
(III) 0.25 |
|
(C) $P(A ∪ B)$ |
(I) 0.5 |
|
(D) $P(A')$ |
(II) 0.8 |
Given:
$P(A) = 0.2$, $P(B) = 0.4$, $P(B|A) = 0.5$
(A) $P(A \cap B) = P(A) \cdot P(B|A) = 0.2 \cdot 0.5 = 0.1$ ⇒ Match with (IV)
(B) $P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.1}{0.4} = 0.25$ ⇒ Match with (III)
(C) $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.2 + 0.4 - 0.1 = 0.5$ ⇒ Match with (I)
(D) $P(A') = 1 - P(A) = 1 - 0.2 = 0.8$ ⇒ Match with (II)