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 that the student is studying mathematics and B be the event that the student is studying biology.
$\text{Then P(A)}=\frac{40}{100}=\frac{2}{5}\text{and}P\left(B\right)=\frac{300}{100}=\frac{3}{10}P(A\cap B)=\frac{10}{100}=\frac{1}{10}\text{We know that}P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=\frac{2}{5}+\frac{3}{10}-\frac{1}{10}=\frac{4+3-1}{10}=\frac{6}{10}=\frac{3}{5}.$