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Question
Mark the correct alternative in the following question:
In a college 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she failed in Mathematics is
Options
\[ \frac{1}{10}\]
\[\frac{1}{3}\]
\[ \frac{2}{5} \]
\[ \frac{9}{20}\]
Solution
\[\text{ Let A be the event of choosing a student failed in Physics and } \]
\[\text{ B be the event of choosing a student failed in Mathematics } . \]
\[\text{ We have } , \]
\[P\left( A \right) = 30 % = \frac{30}{100} = \frac{3}{10}, \]
\[P\left( B \right) = 25 % = \frac{25}{100} = \frac{1}{4} and\]
\[P\left( A \cap B \right) = 10 % = \frac{10}{100} = \frac{1}{10}\]
\[\text{ Now } , \]
\[P\left( A|B \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]
\[ = \frac{\left( \frac{1}{10} \right)}{\left( \frac{1}{4} \right)}\]
\[ = \frac{4}{10}\]
\[ = \frac{2}{5}\]
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