Question

Given \(P(A) = p_1, P(B) = p_2\) and \(P(AB) = p_3\). Then \(P(A' \cap B')\) will be:

• A. \(1 - p_1 - p_2\)
• B. \(1 - p_3\)
• C. \(1 - p_1 p_2 p_3\)
• D. \(1 - p_1 - p_2 + p_3\)

Hint:

To quickly find the probability that neither event occurs, calculate \(1 - P(\text{at least one event occurs})\).
This is always \(1 - P(A \cup B)\), which expands easily using the addition rule.

Answer 1

The Correct Option is D