Question

Mark the correct alternative in each of the following:

A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is

(a) $\frac{1}{5}$ (b) $\frac{3}{25}$ (c) $\frac{4}{25}$ (d) $\frac{2}{25}$ [CBSE 2014]

Answer 1

The total number of cards in the bag is 25.

∴ Total number of outcomes = 25

The numbers from 1 to 25 which are divisible by both 2 and 3 are 6, 12, 18 and 24.

So, the favourable number of outcomes are 4.

∴ P(number on the drawn card is divisible by both 2 and 3) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{4}{25}$

Hence, the correct answer is option C.