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 has passed in Mathematics?

Answer 1

Let event $A\to$ She passes in Mathematics

Let event $B\to$ She passes in computer sciences

$P\left(A\right)=\frac{4}{5}$

$P(A\cap B)=\frac{1}{2}$

To calculate $\to P\left(\frac{B}{A}\right)$

Using Bayes theorem,

$P(A\cap B)=P\left(\frac{B}{A}\right)\cdot P\left(A\right)$

$\Rightarrow P\left(\frac{B}{A}\right)=\frac{1/2}{4/5}=\frac{5}{8}$