Question

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7?

• A. $\frac{5}{8}$
• B. $\frac{3}{8}$
• C. $\frac{2}{5}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{2}{5}$

Out of the integers from 1 to 20,
Multiples of 3: 3, 6, 9, 12, 15, 18
Multiples of 7: 7, 14
Thus multiples of 3 or 7 are 3, 6, 7, 9, 12, 14, 15, 18, i.e., 8 numbers.

Hence, the required probability
$\frac{\text{Number of multiples of 3 or 7 from 1 to 20}}{\text{Number of integers from 1 to 20}}=\frac{8}{20}=\frac{2}{5}$.