Page 71 - Probability Demystified

60 CHAPTER 4 The Multiplication Rules

c. There are 3 green balls and 5 blue balls, so the probability of selecting
a green ball and then a blue ball with replacement is
Pðgreen and blueÞ¼ PðgreenÞ PðblueÞ
3 5
¼
10 10
15 3
¼ ¼
100 20
The multiplication rule can be extended to 3 or more events that
occur in sequence, as shown in the next example.

EXAMPLE: A die is tossed 3 times. Find the probability of getting three 6s.

SOLUTION:
1
When a die is tossed, the probability of getting a six is ; hence, the probabil-
6
ity of getting three 6s is
Pð6 and 6 and 6Þ¼ Pð6Þ Pð6Þ Pð6Þ
1 1 1
¼
6 6 6
1
¼
216
Another situation occurs in probability when subjects are selected from a
large population. Even though the subjects are not replaced, the probability
changes only slightly, so the change can be ignored. Consider the next
example.

EXAMPLE: It is known that 66% of the students at a large college favor
building a new fitness center. If two students are selected at random, find the
probability that all of them favor the building of a new fitness center.

SOLUTION:
Since the student population at the college is large, selecting a student
does not change the 66% probability that the next student selected will
favor the building of a new fitness center; hence, the probability of selecting
two students who both favor the building of a new fitness center is
(0.66)(0.66) ¼ 0.4356 or 43.56%.