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Question
If P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).
Solution
\[\text{ Given } : \]
\[P\left( A \right) = 0 . 4\]
\[P\left( B \right) = 0 . 3\]
\[P\left( B/A \right) = 0 . 5\]
\[\text{ Now } , \]
\[P\left( B/A \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ \Rightarrow 0 . 5 = \frac{P\left( A \cap B \right)}{0 . 4}\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 2\]
\[\]
\[P\left( A/B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)} = \frac{0 . 2}{0 . 3} = \frac{2}{3}\]
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