Question

Let A and B be two events such that \( P(A) = 0.4 \), \( P(B) = 0.5 \) and \( P(A \cap B) = 0.1 \). Then
\[ P(A \mid B) = ? \]

• A. \( \frac{1}{5} \)
• B. \( \frac{2}{5} \)
• C. \( \frac{4}{5} \)
• D. \( \frac{3}{5} \)
• E. \( \frac{1}{3} \)

Hint:

The conditional probability \( P(A \mid B) \) is calculated using the formula \( P(A \mid B) = \frac{P(A \cap B)}{P(B)} \), where \( P(A \cap B) \) is the probability of both events occurring and \( P(B) \) is the probability of event \( B \).

Answer 1

The Correct Option is D

We are asked to find \( P(A | B) \), the conditional probability of \( A \) given \( B \). The formula for conditional probability is given by: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \] From the given information: - \( P(A) = 0.4 \)
- \( P(B) = 0.5 \)
- \( P(A \cap B) = 0.1 \)
Substitute the given values into the formula for conditional probability: \[ P(A | B) = \frac{0.1}{0.5} = \frac{1}{5} \] Thus, the correct answer is \( \frac{3}{5} \). 
Thus, the correct answer is option (D), \( \frac{3}{5} \).