Question

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

Answer 1

Step 1: Finding the number of favorable outcomes and the number of total outcomes.

There are $52$ cards in a deck.

So, the total outcomes will be $52$.

There are $4$ king cards and $4$ queen cards in a deck of $52$ cards.

The favorable outcomes will be all cards except the king and queen cards.

It is obtained as $52-(4+4)=44$.

Step 2: Compute the probability that the card drawn is neither a king nor a queen.

The formula to compute the probability is expressed as,

$Probability=\frac{No.offavorableoutcomes}{Totaloutcomes}$

Substitute the favorable outcomes as $44$ and the total outcomes as $52$ in the formula.

$$\begin{gathered} \Rightarrow P\left(neitherakingnoraqueen\right)=\frac{44}{52} \\ \therefore P\left(neitherakingnoraqueen\right)=\frac{11}{13} \end{gathered}$$

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