Question

Out of $100$ students in a certain class, $70$ students like Mathematics, $40$ students like Science and $15$ students like both Mathematics and Science. A student is selected at random. Find the probability that the student likes Mathematics or Science.

Answer 1

Total number of students in the class $=100$

$\therefore$ $n\left(S\right)=100$

Let $A$ be the event that students like Mathematics

$\therefore$ $n\left(A\right)=70$

$\therefore$ $P\left(A\right)=\frac{70}{100}$

Let $B$ be the event that students like Science

$\therefore$ $n\left(B\right)=40$

$\therefore$ $P\left(B\right)=\frac{40}{100}$

$A\cap B$ is the event when students like both Mathematics and Science

$\therefore$ $n(A\cap B)=15$

$\therefore$ $P(A\cap B)=\frac{15}{100}$

To find the probability that the student likes Mathematics or Science

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{70}{100}+\frac{40}{100}-\frac{15}{100}$

$=\frac{70+40-15}{100}$

$=\frac{95}{100}=\frac{19}{20}$