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Question
Choose the correct alternative in the following question:
If A and B are two events associated to a random experiment such that \[P\left( A \cap B \right) = \frac{7}{10} \text{ and } P\left( B \right) = \frac{17}{20}\] , then P(A|B) =
Options
`14/17`
` 17/20`
`7/8 `
` 1/8`
Solution
We have,
\[P\left( A \cap B \right) = \frac{7}{10} \text { and } P\left( B \right) = \frac{17}{20}\]
\[\text{ Now } , \]
\[P\left( A|B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]
\[ = \frac{\left( \frac{7}{10} \right)}{\left( \frac{17}{20} \right)}\]
\[ = \frac{7 \times 20}{17 \times 10}\]
\[ = \frac{14}{17}\]
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