Chapter 8.6, Problem 42E

To determine

To find: the probability of the union of the two events.

Answer to Problem 42E

The probability that the card is face or black is $\frac{8}{13}$ .

Explanation of Solution

Given information:

One card is selected at random from a standard deck of 52 playing cards.

The card is a face card or a black card.

Calculation:

A card is drawn at random from a standard deck of 52 playing cards.

Probability of the union of two events is,

  $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

There are total 12 face cards and 26 black cards while 6 cards is both face and black.

So, the probability that the card is face card or a black card is,

  $\begin{array}{c}P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\\ =\frac{12}{52}+\frac{26}{52}-\frac{6}{52}\\ =\frac{32}{52}\\ =\frac{8}{13}\end{array}$

Hence, the probability that the card is a face card or a black card is $\frac{8}{13}$ .