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 selected at random. Find the
probability that the student like Mathematics or Science.​

Answer 1

Total number of students in the class =100

∴ n(S)=100

Let A be the event that students like Mathematics,

∴ n(A)=70

$∴ P(A)= \frac{70}{100}$

Let B be the event that students like Science

∴ n(B)=40

$∴ P(B)= \frac{40}{100}$

A∩B is the event when students like both Mathematics and Science

∴ n(A∩B)=15

$∴ P(A∩B)= \frac{15}{100}$

To find the probability that the student likes Mathematics or Science

P(A∪B)=P(A)+P(B)−P(A∩B)

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

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

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