Question

Mark the correct alternative in each of the following:

A card is drawn at random from a pack of 52 cards. The probability that the drawn card is not an ace is

(a) $\frac{1}{13}$ (b) $\frac{9}{13}$ (c) $\frac{4}{13}$ (d) $\frac{12}{13}$ [CBSE 2014]

Answer 1

Total number of possible outcomes = 52

There are 4 ace cards in a pack of cards.

∴ Number of non ace cards in the pack of cards = 52 − 4 = 48

So, the favourable number of outcomes are 48.

∴ P(drawn card is not an ace card) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{48}{52}=\frac{12}{13}$

Hence, the correct answer is option D.