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Question
The probability that a student selected at random from a class will pass in Mathematics is `4/5`, and the probability that he/she passes in Mathematics and Computer Science is `1/2`. What is the probability that he/she will pass in Computer Science if it is known that he/she has passed in Mathematics?
Solution
Consider the given events.
M = Students passes Mathematics
C = Students passes Computer Science
\[\text{ We have } , \]
\[P\left( M \right) = \frac{4}{5} \]
\[P\left( M \cap C \right) = \frac{1}{2}\]
\[\text{ Now } , \]
\[P\left( \frac{C}{M} \right) = \frac{P\left( M \cap C \right)}{P\left( M \right)}\]
\[ = \frac{\frac{1}{2}}{\frac{4}{5}} = \frac{5}{8}\]
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