Question

(d) If \( P(A) = 0.5 \), \( P(B) = 0.4 \), and \( A \) and \( B \) are independent events, then find the values of (A) \( P(A \cap B) \) and (B) \( P(A \cup B) \).

Hint:

For independent events, multiply probabilities for \( P(A \cap B) \) and use the union formula for \( P(A \cup B) \).

Answer 1

(A) For independent events:

\[ P(A \cap B) = P(A) \cdot P(B) = 0.5 \cdot 0.4 = 0.2. \]

(B) Using the formula:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \]

Substituting values:

\[ P(A \cup B) = 0.5 + 0.4 - 0.2 = 0.7. \]