Question

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

Answer 1

Determining the probability:

We know that a deck has $52$ cards.

So, the total number of outcomes $=52$.

A deck of cards has are $4$ king and $4$ queen cards.

So, the total number of favorable outcomes

$$\begin{gathered} =totalcards-\left(kingcards+queencards\right) \\ =52-8 \\ =44 \end{gathered}$$

The formula for probability is

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

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