Question

If \( P(A \cup B) = 0.9 \) and} \( P(A \cap B) = 0.4 \), then \( P(A) + P(B) \) is:

• A. \( 0.3 \)
• B. \( 1 \)
• C. \( 1.3 \)
• D. \( 0.7 \)

Hint:

When calculating the probability of the union of two events, make sure to subtract the intersection to avoid double-counting the outcomes that are common to both events.

Answer 1

The Correct Option is C

Given probabilities are: \( P(A \cup B) = 0.9 \) and \( P(A \cap B) = 0.4 \). The sum \( P(A) + P(B) \) is calculated using the inclusion-exclusion principle: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \). This formula ensures that the union probability correctly reflects the individual probabilities of A and B, accounting for their overlap. Substituting the given values: \( 0.9 = P(A) + P(B) - 0.4 \). Rearranging to solve for \( P(A) + P(B) \): \( P(A) + P(B) = 0.9 + 0.4 = 1.3 \). Thus, \( P(A) + P(B) = 1.3 \), corresponding to option (C).