STRATEGY: There are 4 outcomes in the sample space and two outcomes
(HT, TH) in the event.
IMPLEMENTATION:P¼(one head and one tail)¼
2
4
¼
1
2
.
EVALUATION: Looking at the sample space, it is obvious that the prob-
ability of 2 choices from four outcomes is^12.
When two dice are rolled, each die can have one of six outcomes.
Therefore, there are 6 6 ¼36 outcomes in the sample space. The outcomes
can be arranged in ordered pairs such that the first number is the number
of spots on the first die, and the second number in the pair is the number
of spots on the second die. For example, the ordered pair (2, 4) means a 2
came up on the first die and a 4 came up on the second die. Also, the sum of
the numbers for this outcome is 2þ 4 ¼6.
The sample space for two dice is shown next:
ð1, 1Þð1, 2Þð1, 3Þð1, 4Þð1, 5Þð1, 6Þ
ð2, 1Þð2, 2Þð2, 3Þð2, 4Þð2, 5Þð2, 6Þ
ð3, 1Þð3, 2Þð3, 3Þð3, 4Þð3, 5Þð3, 6Þ
ð4, 1Þð4, 2Þð4, 3Þð4, 4Þð4, 5Þð4, 6Þ
ð5, 1Þð5, 2Þð5, 3Þð5, 4Þð5, 5Þð5, 6Þ
ð6, 1Þð6, 2Þð6, 3Þð6, 4Þð6, 5Þð6, 6ÞEXAMPLE:Two dice are rolled; find the probability of getting a sum of 9.
SOLUTION:
GOAL: You are being asked to find the probability of getting a sum of 9.
STRATEGY: There are 36 outcomes in the sample space and four ways to
get a sum of nine. They are (3, 6), (4, 5), (5, 4), and (6, 3).
IMPLEMENTATION:P(sum of 9)¼
4
36
¼
1
9
.
EVALUATION: Use the sample space to verify your answer.
EXAMPLE:Two dice are rolled; find the probability of getting a sum less
than 4.
LESSON 22 Word Problems in Probability 269