Question

If A and B are events such that P (A) = 0.6, P (B) = 0.3 and P (A ∩ B) = 0.2, find P (A/B) and P (B/A).

Answer 1

\[\text{ Given } : \]
\[P\left( A \right) = 0 . 6\]
\[P\left( B \right) = 0 . 3 \]
\[P\left( A \cap B \right) = 0 . 2\]
\[ \text{ Now } , \]
\[P\left( \frac{A}{B} \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]
\[ \Rightarrow P\left( \frac{A}{B} \right) = \frac{0 . 2}{0 . 3} = \frac{2}{3}\]
\[P\left( \frac{B}{A} \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ \Rightarrow P\left( \frac{B}{A} \right) = \frac{0 . 2}{0 . 6} = \frac{1}{3}\]