Question

If \( A \) and \( B \) are two independent events such that \( P(A) = 0.3 \), \( P(B) = x \), and \( P(A \cup B) = 0.44 \), then \( x = \):

• A. \( 0.1 \)
• B. \( 0.4 \)
• C. \( 0.3 \)
• D. \( 0.2 \)

Hint:

Probability with Independence}
For independent events: \( P(A \cup B) = P(A) + P(B) - P(A)P(B) \)
Carefully isolate and solve for unknown probability
Ensure logic fits independence assumption

Answer 1

The Correct Option is D

Using the formula for independent events: \[ P(A \cup B) = P(A) + P(B) - P(A)P(B) \Rightarrow 0.44 = 0.3 + x - 0.3x \Rightarrow 0.44 = 0.3 + x(1 - 0.3) = 0.3 + 0.7x \Rightarrow 0.14 = 0.7x \Rightarrow x = \frac{0.14}{0.7} = 0.2 \]