Question

In Class $XI$ of a school $40$% of the students study Mathematics and $30$% study Biology, $10$% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Answer 1

Let $A$ be the event in which the selected student studies Mathematics and $B$ be the event in which the selected student studies Biology
Accordingly $P\left(A\right)=40$% $=\frac{40}{100}=\frac{2}{5}$
$P\left(B\right)=30$% $=\frac{30}{100}=\frac{3}{10}$
$P\left(AorB\right)=10$% $=\frac{10}{100}=\frac{1}{10}$
We know that $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P(A$ and $B)$
$\therefore P\left(AorB\right)=\frac{2}{5}+\frac{3}{10}-\frac{1}{10}=\frac{6}{10}=0.6$
Thus the probability that the selected student will be studying Mathematics or Biology is $0.6$