College Algebra, Chapter 10, Review Exercises, Section Review Exercises, Problem 28

Find the probability that the indicated card is drawn at random form a 52-card deck.

a.) An ace

There are four aces in a deck of a card. Thus, the probability in this case is

$\displaystyle \frac{4}{52} = \frac{1}{13}$

b.) An ace or a jack

Since an ace can never be jack, then the probability of this mutually exclusive event is

$\displaystyle \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13}$

c.) An ace or a spade

Since there is an ace of spades we have an intersection of two events. Thus, the probability of union of this two events is

$\displaystyle \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{4}{13}$

d.) A red ace

We know that there are only two red aces. Precisely ace of diamonds and ace of hearts. Thus, the probability in this case is

$\displaystyle \frac{2}{52} = \frac{1}{26}$