Question

From a well-shuffled pack of $52$ cards, three kings and one ace are removed. From the remaining cards, a card is drawn at random. Find the probability that the card drawn is neither a jack nor a queen.

Answer 1

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

Given that there is a well-shuffled pack of $52$ cards.

Since three kings and an ace are removed,

$52-3-1=48$

So, the total number of outcomes will be $48$.

In a pack of $52$ cards, there are $26$ red cards and $26$ black cards.

There are four suits - Heart, Diamond, Club and Spade having $13$ cards each.

There are four face cards - ace, king, queen and jack in each suit.

So, the number of cards that are neither jack nor queen would be

$$\begin{gathered} Remainingcards-jackcards-queencards \\ \Rightarrow 48-4-4 \\ \Rightarrow 40 \end{gathered}$$

So, the number of favorable outcomes is $40$.

Step 2 Finding the probability of drawing a card that is neither a jack nor a queen:

The formula for probability is

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

$$\begin{gathered} \Rightarrow P(neitherajacknoraqueen)=\frac{40}{48} \\ \therefore P(neitherajacknoraqueen)=\frac{5}{6} \end{gathered}$$

Hence, the probability of drawing a card that is neither a jack nor a queen is $\frac{5}{6}$.