Question

A card is drawn at random from a pack of $52$ playing cards. Find the probability that the card drawn is neither a queen nor a jack.

Answer 1

Step 1: Finding the probability of getting a queen nor a jack :

There are $52$ cards in the pack.

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

Let $A$ be the event of drawing a card which is either a queen or jack.

In a total number of $52$ cards, we have $4$ queens and $4$ jacks.

$n\left(A\right)=4+4=8.$

$$\begin{gathered} \Rightarrow Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \therefore P(aqueenorjack)=\frac{8}{52} \end{gathered}$$

Step 2: Finding the probability of getting neither a queen nor a jack :

Let $E$ be the event of drawing a card neither a queen nor jack.

$$\begin{gathered} P\left(E\right)=1-P\left(A\right) \\ =1-\left(\frac{8}{52}\right) \\ =\left(\frac{52-8}{52}\right) \\ =\frac{44}{52} \\ =\frac{11}{13} \end{gathered}$$

Hence, the required probability of getting neither a queen nor a jack is $\frac{11}{13}.$