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?

Answer 1

Consider the given events.
M = Students passes Mathematics
C = Students passes Computer Science

\[\text{ We have } , \]

\[P\left( M \right) = \frac{4}{5} \]

\[P\left( M \cap C \right) = \frac{1}{2}\]

\[\text{ Now } , \]

\[P\left( \frac{C}{M} \right) = \frac{P\left( M \cap C \right)}{P\left( M \right)}\]

\[ = \frac{\frac{1}{2}}{\frac{4}{5}} = \frac{5}{8}\]