Question

If \( P(A) = \frac{1}{5}, P(B) = \frac{3}{5} \) and \( P(A \cap B) = \frac{2}{5} \), then \( P(A' \cup B') \) is :

• A. \( \frac{19}{25} \)
• B. \( \frac{9}{25} \)
• C. \( \frac{19}{25} \)
• D. \( \frac{5}{13} \)

Hint:

The probability of the union of two events can be found by \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).

Answer 1

The Correct Option is A

We know that \( P(A' \cup B') = 1 - P(A \cap B) \). Thus, \[ P(A' \cup B') = 1 - \frac{2}{5} = \frac{19}{25} \] So, the correct answer is \( \frac{19}{25} \).