Question

Let $ A $ and $ B $ be two independent events, then $ P(A \cap B') = $

• A. \( P(A) \cdot P(B') \)
• B. \( P(A) \cdot P(B) \)
• C. \( P(A) - P(A \cup B) \)
• D. \( P(B) \cdot P(A') \)

Hint:

For independent events, the probability of the intersection of an event and the complement of another event is the product of the probabilities of the events.

Answer 1

The Correct Option is A

For two independent events \( A \) and \( B \), the probability of their intersection with the complement of \( B \) is: \[ P(A \cap B') = P(A) \cdot P(B') \] This follows from the independence of \( A \) and \( B \), meaning the occurrence of one does not affect the probability of the other.
Therefore, the correct answer is 1. \( P(A) \cdot P(B') \).