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Question
If P (A) = 0.4, P (B) = 0.8, P (B/A) = 0.6. Find P (A/B) and P (A ∪ B).
Solution
\[\text{ Given } : \]
\[P\left( A \right) = 0 . 4\]
\[P\left( B \right) = 0 . 8 \]
\[P\left( B/A \right) = 0 . 6\]
\[\text{ Now } 0, \]
\[P\left( B/A \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ \Rightarrow 0 . 6 = \frac{P\left( A \cap B \right)}{0 . 4}\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 24\]
\[P\left( A/B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)} = \frac{0 . 24}{0 . 8} = 0 . 3\]
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow P\left( A \cup B \right) = 0 . 4 + 0 . 8 - 0 . 24 = 0 . 96\]
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