Question

A card is drawn at random from a pack of $52$ playing cards. Find the probability that the card drawn is neither an ace nor a black king.

Answer 1

Step 1: Find the number of favourable outcomes:

The total number of playing cards in a pack $=52$

The total number of aces in a pack $=4$

The total number of kings in a pack $=4$

There are two black kings and two red kings in a pack of playing cards.

Therefore, the total number of black kings in a pack of cards will be $2$.

Thus, the number of favourable outcomes to the given event is $52-4-2=46$.

Step 2: Use the formula for probability:

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$$\begin{gathered} \text{Probability=}\frac{46}{52} \\ \mathrm{Probability}\text{=}\frac{23}{26} \end{gathered}$$

Final answer:

Hence, the probability that the card drawn is neither an ace nor a black king is $\frac{23}{26}$.