Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| (A) | If \( A \) and \( B \) are mutually exclusive events then \( P(A\cup B)= \) | (I) | \( \displaystyle\frac{P(A\cap B)}{P(B)},P(B)\ne 0 \) |
| (B) | If \( A \) and \( B \) are independent events then \( P(A\cap B)= \) | (II) | \( \displaystyle\frac{P(A\cap B)}{P(A)},P(A)\ne 0 \) |
| (C) | If \( A \) and \( B \) are two events of a sample space of an experiment, then \( P(A/B)= \) | (III) | \( P(A)\cdot P(B) \) |
| (D) | If \( A \) and \( B \) are two events of a sample space of an experiment, then \( P(B/A)= \) | (IV) | \( P(A)+P(B) \) |
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)
Each item is a standard definition or rule of probability.
(A) If A and B are mutually exclusive events then P(A ∪ B) =
This matches (IV) \( P(A)+P(B) \).
By the addition rule \( P(A\cup B)=P(A)+P(B)-P(A\cap B) \), and mutually exclusive events have \( P(A\cap B)=0 \).
(B) If A and B are independent events then P(A ∩ B) =
This matches (III) \( P(A)\cdot P(B) \).
This is the definition of independent events.
(C) If A and B are two events of a sample space of an experiment, then P(A/B) =
This matches (I) \( \frac{P(A\cap B)}{P(B)},P(B)\ne 0 \).
In the conditional probability of A given B, the event B is the reduced sample space, so we divide by P(B).
(D) If A and B are two events of a sample space of an experiment, then P(B/A) =
This matches (II) \( \frac{P(A\cap B)}{P(A)},P(A)\ne 0 \).
Here A is the given event, so we divide by P(A).
So the matching is (A)-(IV), (B)-(III), (C)-(I), (D)-(II).