Question

If \( P(A) = 0.12, P(B) = 0.15 \) and \( P(B/A) = 0.18 \), then find the value of \( P(A \cap B) \).

Hint:

{Formula:} \[ P(B/A) = \frac{P(A \cap B)}{P(A)} \quad \Rightarrow \quad P(A \cap B) = P(A) \times P(B/A) \] Always ensure probabilities are in decimal form before multiplication.

Answer 1

The given values are:
\( P(A) = 0.12 \), \( P(B) = 0.15 \), and \( P(B/A) = 0.18 \). We are asked to find \( P(A \cap B) \), which represents the probability of both events \( A \) and \( B \) occurring.

By the definition of conditional probability, we have: \[ P(B/A) = \frac{P(A \cap B)}{P(A)} \] Rearranging the equation to find \( P(A \cap B) \): \[ P(A \cap B) = P(B/A) \times P(A) \] Substituting the given values: \[ P(A \cap B) = 0.18 \times 0.12 \] \[ P(A \cap B) = 0.0216 \] Final Answer:
The value of \( P(A \cap B) \) is \( \boxed{0.0216} \).