College Algebra, Chapter 10, 10.3, Section 10.3, Problem 12

Suppose that a card is drawn randomly from a standard 52-card deck. Find the probability of the given event.

a.) The card drawn is a heart.

There are four different suits on the cards namely hearts, spades, diamonds and clubs. Each of which has 13 cards. So the probability of drawing a heart is

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

b.) The card drawn is either a heart or a spade.

The probability of drawing a heart or a spade is

$\displaystyle \frac{13}{52} + \frac{13}{52} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

c.) The card drawn is a heart, a diamond, or a spade.

In this case, we can use the probability of the complement of an event. If we get the probability of getting a club, we have

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

Thus, the probability of getting a heart, a diamond or a spade is

$\displaystyle 1 - \frac{1}{4} = \frac{3}{4}$