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.
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 $P ( A$ and $B )= P ( A )+ P ( B )- P ( A $ and $B )$
$\therefore P(A $ or $ 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 $0.6$.
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