Question

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is either a king or 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 are $52$.

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

So, the favorable outcomes are $4+4=8$.

Step 2: Compute the probability that the card drawn is either a king or a queen.

The formula to compute the probability is expressed as,

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

Substitute the number of favorable outcomes as $8$ and the total number of outcomes as $52$ in the formula.

$$\begin{gathered} \Rightarrow P\left(eitherakingoraqueen\right)=\frac{8}{52} \\ \therefore P\left(eitherakingoraqueen\right)=\frac{2}{13} \end{gathered}$$

Therefore, the probability that the card drawn is either a king or a queen is $\frac{2}{13}$.