Question

The probability that a student selected at random from a class will pass in Mathematics is $\frac{4}{5},$ and the probability that he/she passes in Mathematics and Computer Science is $\frac{1}{2}$. 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

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ P\left(M\right)=\frac{4}{5} \\ P\left(M\cap C\right)=\frac{1}{2} \\ \mathrm{Now}, \\ P\left(\raisebox{1ex}{$C$}\!\left/ \!\raisebox{-1ex}{$M$}\right.\right)=\frac{P\left(M\cap C\right)}{P\left(M\right)} \\ =\frac{\frac{1}{2}}{\frac{4}{5}}=\frac{5}{8} \end{gathered}$$