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.
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, $P(A)=40 \%=\frac{40}{100}=\frac{2}{5}$
$P(B)=30 \%=\frac{30}{100}=\frac{3}{10}$
$P(A$ and $B)=10 \%=\frac{10}{100}=\frac{1}{10}$
We know that P(A or B) = P(A) + P(B) – P(A and B)
$\therefore \mathrm{P}(\mathrm{A}$ or $\mathrm{B})=\frac{2}{5}+\frac{3}{10}-\frac{1}{10}=\frac{6}{10}=0.6$
Thus, the probability that the selected student will be studying Mathematics or Biology is 0.6.