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Question
Mark the correct alternative in the following question:
\[\text{ Let A and B be two events . If } P\left( A \right) = 0 . 2, P\left( B \right) = 0 . 4, P\left( A \cup B \right) = 0 . 6, \text{ then } P\left( A|B \right) \text{ is equal to} \]
Options
0 . 8
0 . 5
0 . 3
0
Solution
\[\text{ We have } , \]
\[P\left( A \right) = 0 . 2, P\left( B \right) = 0 . 4 \text{ and } P\left( A \cup B \right) = 0 . 6\]
\[\text{ As } , P\left( A \cup B \right) = 0 . 6\]
\[ \Rightarrow P\left( A \right) + P\left( B \right) - P\left( A \cap B \right) = 0 . 6\]
\[ \Rightarrow 0 . 2 + 0 . 4 - P\left( A \cap B \right) = 0 . 6\]
\[ \Rightarrow 0 . 6 - P\left( A \cap B \right) = 0 . 6\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 6 - 0 . 6\]
\[ \Rightarrow P\left( A \cap B \right) = 0\]
\[\text{ Now } , \]
\[P\left( A|B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)} = \frac{0}{0 . 4} = 0\]
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