Chapter 8.6, Problem 43E

To determine

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

Answer to Problem 43E

The probability that the card is 5 or 2 is $\frac{2}{13}$ .

Explanation of Solution

Given information:

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

The card is a 5 or 2.

Calculation:

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

Probability of the union of two events is,

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

There are total 4 numbers of 5number card and 4 numbers of 2 number card while no card is common between 5 and 2.

So, the probability that the card is a 5 or 2 is,

  $\begin{array}{c}P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)\\ =\frac{4}{52}+\frac{4}{52}\\ =\frac{8}{52}\\ =\frac{2}{13}\end{array}$

Hence, the probability that the card is a 5 or 2 is $\frac{2}{13}$ .