Question

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is: a king or a jack, a non-ace, a red card, neither a king nor a queen.

Answer 1

Step 1: Use the formula for probability and find the total number of outcomes:

The formula for probability is,

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Given that, a card is drawn from a well-shuffled deck of playing cards.

Thus, the total number of outcomes will be $52.$

Step 2: Find the probability of the card drawn is a king or a jack:

The total number of cards is $52$

We have, $4$ kings and $4$ jacks

Therefore, the probability is

$$\begin{gathered} P=\frac{4+4}{52} \\ =\frac{8}{52} \\ =\frac{2}{13} \end{gathered}$$

Step 3: Find the probability of the card drawn is a non-ace:

The total number of cards is $52$

we have $4$ aces

To find the non-aces$=52-4=48$

$$\begin{gathered} P(non-ace)=\frac{48}{52} \\ P(non-ace)=\frac{12}{13} \end{gathered}$$

Step 4: Find the probability of the card drawn is a red card:

We have, the number red cards is $26$

Therefore, the probability is

$$\begin{gathered} P=\frac{26}{52} \\ P=\frac{1}{2} \end{gathered}$$

Step 5: Find the probability of the card drawn is neither a king nor a queen:

We have $4$ kings and $4$ queens

Therefore, the probability is

$$\begin{gathered} P=\frac{52-4-4}{52} \\ P=\frac{44}{52} \\ P=\frac{11}{13} \end{gathered}$$

Hence, from the above conclusions, the probability that the card drawn is a king or a jack is $\frac{2}{13}$, a non-ace is $\frac{12}{13}$, a red card is $\frac{1}{2}$, andneither a king nor a queen is $\frac{11}{13}$