Page 45 - Probability Demystified

34 CHAPTER 2 Sample Spaces

ANSWERS

1. There are 52 outcomes in the sample space.
a. There are four 9s, so
4 1
Pð9Þ¼ ¼
52 13
b. There is only one ace of diamonds, so
1
PðA ^Þ¼
52
c. There are 13 clubs, so
13 1
Pð¨Þ¼ ¼
52 4

2. There are 52 outcomes in the sample space.
a. There are 26 black cards: they are 13 clubs and 13 spades, so
26 1
Pðblack card) ¼ ¼
52 2
b. There are two red queens: they are the queen of diamonds and the
queen of hearts, so
2 1
Pðred queen) = ¼
52 26
c. There are 13 hearts and 13 spades, so
26 1
Pð˘ or ¨Þ¼ ¼
52 2

3. There are 52 outcomes in the sample space.
a. There are 13 diamonds and 12 face cards, but the jack, queen, and
king of diamonds have been counted twice, so

13 þ 12 4 21
P(diamond or face card) ¼ ¼
52 52
b. There are 13 clubs and four 8s, but the 8 of clubs has been
counted twice, so
13 þ 4 1 16 4
Pð¨ or an 8Þ¼ ¼ ¼
52 52 13