Question

Let \(A, B\) be two events and \(\overline{A}\) be the complement of \(A\). If \(P(A) = 0.7\), \(P(B) = 0.7\) and \(P(B \mid A) = 0.5\), then \(P(A \cup B) = \_\_\_.\)

• A. 0.65
• B. 0.85
• C. 0.75
• D. 0.50

Hint:

To solve probability problems, remember the formula for the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

Answer 1

The Correct Option is C

We use the formula for the probability of the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Now, we need to calculate $P(A \cap B)$: \[ P(A \cap B) = P(B|A) \cdot P(A) = 0.5 \cdot 0.7 = 0.35 \] Now substitute the values into the formula for $P(A \cup B)$: \[ P(A \cup B) = 0.7 + 0.7 - 0.35 = 0.75 \]