Question

If \( A \) and \( B \) are two independent events such that \( P(A) = 0.4 \) and \( P(A \cup B) = 0.7 \), then \( P(B) \) is equal to:

• A. 0.3
• B. 0.4
• C. 0.5
• D. 0.6
• E. 0.7

Hint:

When dealing with independent events, use the multiplication rule to calculate the intersection probability.

Answer 1

The Correct Option is C

Using the formula for the probability of the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Since \( A \) and \( B \) are independent events: \[ P(A \cap B) = P(A) \cdot P(B) \] Substitute the values: \[ 0.7 = 0.4 + P(B) - 0.4 \cdot P(B) \] Simplify the equation: \[ 0.7 = 0.4 + P(B)(1 - 0.4) \] \[ 0.7 = 0.4 + 0.6P(B) \] \[ 0.3 = 0.6P(B) \] \[ P(B) = \frac{0.3}{0.6} = 0.5 \]