Question

From a well-shuffled pack of $52$ cards, two black kings and two blackjacks are removed. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is neither an ace nor a king.

Answer 1

Step 1: Find the number of favorable outcomes

Total number of cards in a deck $=52$

Given: Two black kings and two blackjacks are removed.

Therefore, The total outcomes $n\left(s\right)=53-(2+2)=48$

We shall find the probability that the drawn card is neither an ace nor a king.

Number of aces $=4$

Number of kings left $=2$

Thus, number of favorable outcomes $n\left(E\right)=48-(4+2)=42$

Step 2: Finding the probability

$$\begin{gathered} P\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)} \\ =\frac{42}{48} \\ =\frac{7}{8} \end{gathered}$$

Final answer:

Thus the probability that the card drawn is neither an ace nor a king is $\frac{7}{8}$