Question

From a set of 18 cards, numbered 1, 2, 3, .....,17, 18 one card is drawn. What is the probability that the number on the card is multiple of 3 or 7?

• A. $\frac{5}{17}$
• B. $\frac{4}{9}$
• C. $\frac{8}{17}$
• D. $\frac{6}{17}$

Answer 1

The correct option is B

$\frac{4}{9}$

Given,

Total number of outcomes = 18

The multiples of 3 are 3, 6, 9, 12, 15, 18

The multiples of 7 are 7, 14.

Thus, the favourable outcomes are 3, 6, 7, 9, 12, 14, 15 and 18

$\Rightarrow$ Number of favourable outcomes = 8

Probability of an event, P(E)$=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

$\Rightarrow$ P(getting multiple of 3 or 7) = $\frac{8}{18}$ = $\frac{4}{9}$

Therefore, probability that the number is multiple of 3 or 7 is $\frac{4}{9}$ .