Question

If A and B are independent events such that \( P(B) = \frac{2}{7} \), \( P(A \cup B) = 0.8 \), then \( P(A) = \)?

• A. 0.1
• B. 0.2
• C. 0.3
• D. 0.4

Hint:

For problems involving independent events, remember that \( P(A \cap B) = P(A)P(B) \), which can simplify your calculations.

Answer 1

The Correct Option is C

The formula for the union of two independent events is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Since \( A \) and \( B \) are independent, \( P(A \cap B) = P(A)P(B) \). Substituting the known values: \[ 0.8 = P(A) + \frac{2}{7} - P(A) \times \frac{2}{7} \] Simplifying this equation: \[ 0.8 = P(A) \left( 1 - \frac{2}{7} \right) + \frac{2}{7} \] \[ 0.8 - \frac{2}{7} = P(A) \times \frac{5}{7} \] \[ \frac{6}{7} = P(A) \times \frac{5}{7} \] \[ P(A) = 0.3 \]