Question

The probability that at least one of \( A \) or \( B \) occurs is 0.6. If \( A \) and \( B \) occur simultaneously with probability 0.2, then \( P(A') + P(B') \) is:

• A. 0.7
• B. 1.5
• C. 1.1
• D. 1.2
• E. 0.3

Hint:

For complementary events, remember that \( P(A') = 1 - P(A) \).

Answer 1

The Correct Option is D

We are given: \[ P(A \cup B) = 0.6, \quad P(A \cap B) = 0.2 \] Using the formula for the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substitute the given values: \[ 0.6 = P(A) + P(B) - 0.2 \] \[ P(A) + P(B) = 0.8 \] Now, \( P(A') + P(B') \) is equal to: \[ P(A') + P(B') = 1 - P(A) + 1 - P(B) = 2 - (P(A) + P(B)) \] \[ P(A') + P(B') = 2 - 0.8 = 1.2 \]