Page 42 - Probability Demystified

CHAPTER 2 Sample Spaces 31

EXAMPLE: A single card is drawn at random from a standard deck of
cards. Find the probability that it is

a. The 4 of diamonds.
b. A queen.
c. A 5 or a heart.

SOLUTION:
a. The sample space consists of 52 outcomes and only one outcome is
the four of diamonds; hence,
1
Pð4 ^Þ¼
52
b. Since there are four queens (one of each suit),
4 1
PðQÞ¼ ¼
52 13
c. In this case, there are 13 hearts and 4 fives; however, the 5˘ has been
counted twice, so the number of ways to get a 5 or a heart is
13 þ 4 1 ¼ 16. Hence,
16 4
Pð5or ˘Þ¼ ¼ :
52 13
A table can be used for the sample space when two dice are rolled. Since
the first die can land in 6 ways and the second die can land in 6 ways, there
are 6 6 or 36 outcomes in the sample space. It does not matter whether the
two dice are of the same color or different color. The sample space is shown
in Figure 2-11.

Fig. 2-11.