Chapter 9.7, Problem 22E

To determine

To calculate: The probability that the card is not a face card when a card is chosen at random from a deck of 52 cards.

Answer to Problem 22E

The probability that the card drawn from a deck of 52 playing cards is not a face card is $\frac{10}{13}$ .

Explanation of Solution

Given information:

A card is chosen at random from a deck of 52 cards.

Formula used:

The probability of an event is the ratio of number of possible outcomes of an event E denoted by $n\left(E\right)$ and the sample space of equally likely outcome denoted by $n\left(S\right)$ . Mathematically it is denoted by, $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ .

Calculation:

Consider that acard is chosen at random from a deck of 52 cards.

In a deck of cards there are 12 face cards.

Therefore, there are 40 non face cards.

Recall that the probability of an event is the ratio of number of possible outcomes of an event E denoted by $n\left(E\right)$ and the sample space of equally likely outcome denoted by $n\left(S\right)$ . Mathematically it is denoted by, $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ .

Denote the event E as drawn card is not a face card. Sample space is 52.

So, $n\left(E\right)=40$ and $n\left(S\right)=52$ .

Probability that a card drawn from a deck of 52 playing card is not a face card is

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{40}{52}\\ =\frac{10}{13}\end{array}$

Thus, the probability that the card drawn from a deck of 52 playing cards is not a face card is $\frac{10}{13}$ .