Question

A card is drawn from a well-shuffled deck of cards. What is the probability that the card drawn is neither a king nor a queen?

Answer 1

Probability:

The total number of cards in a deck is $52$.

Number of king cards$=4$

Number of queen cards$=4$

Total number of king and queen cards$=4+4=8$

Number of cards that are neither king nor queen$=52-8=44$

The probability of a drawn card is neither king nor queen,

$$\begin{gathered} \mathbf{P}\mathbf{\left(}\mathbf{E}\mathbf{\right)}\mathbf{=}\frac{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{favourable}\mathbf{}\mathbf{outcomes}}{\mathbf{Total}\mathbf{}\mathbf{outcomes}} \\ =\frac{44}{52} \\ =\frac{11}{13} \end{gathered}$$

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