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Question
Mark the correct alternative in the following question:
If A and B are two events such that P(A) = \[\frac{4}{5}\] , and \[P\left( A \cap B \right) = \frac{7}{10}\] , then P(B|A) =
Options
`1/10`
`1/8`
`7/8`
`17/20`
Solution
We have ,
\[P\left( A \right) = \frac{4}{5} \text{ and } P\left( A \cap B \right) = \frac{7}{10}\]
\[\text{ Now } , \]
\[P\left( B|A \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]
\[ = \frac{\left( \frac{7}{10} \right)}{\left( \frac{4}{5} \right)}\]
\[ = \frac{7 \times 5}{10 \times 4}\]
\[ = \frac{7}{8}\]
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