Question

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the drawn card is neither a king nor a queen.

Answer 1

Favourable outcomes = 52 − 4kings − 4queens = 44

Total outcomes = 52

$$\begin{gathered} \mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}\mathrm{E}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}} \\ =\frac{44}{52} \\ =\frac{11}{13} \end{gathered}$$

Thus, the probability that the drawn card is neither a king nor a queen is $\frac{11}{13}$.