Page 144 - Probability Demystified

CHAPTER 8 Other Probability Distributions 133

PRACTICE

1. At a swimming pool snack bar, the probabilities that a person buys
one item, two items, or three items are 0.3, 0.4, and 0.3. If six people
are selected at random, find the probability that 2 will buy one item,
3 will buy two items, and 1 will buy three items.
2. A survey of adults who go out once a week showed 60% choose a
movie, 30% choose dinner and a play, and 10% go shopping. If 10
people are selected, find the probability that 5 will go to a movie,
4 will go to dinner and a play, and one will go shopping.
3. A box contains 5 white marbles, 3 red marbles, and 2 green marbles.
If 5 marbles are selected with replacement, find the probability that
2 will be white, 2 will be red, and one will be green.
4. Automobiles are randomly inspected in a certain state. The proba-
bilities for having no violations, 1 violation, and 2 or more violations
are 0.50, 0.30, and 0.20 respectively. If 10 automobiles are inspected,
find the probability that 5 will have no violations, 3 will have one
violation, and 2 will have 2 or more violations.
5. According to Mendel’s theory, if tall and colorful plants are crossed
with short and colorless plants, the corresponding probabilities are
9 , 3 , 3 , and 1 for tall and colorful, tall and colorless, short and
16 16 16 16
colorful, and short and colorless. If 8 plants are selected, find the
probability that 3 will be tall and colorful, 2 will be tall and colorless,
2 will be short and colorful and 1 will be short and colorless.

ANSWERS
1. n ¼ 6, x 1 ¼ 2, x 2 ¼ 3, x 3 ¼ 1, and p 1 ¼ 0.3, p 2 ¼ 0.4, and p 3 ¼ 0.3

6!
2
3
1
The probability is ð0:3Þ ð0:4Þ ð0:3Þ ¼ 60ð0:001728Þ¼ 0:10368
2!3!1!
2. n ¼ 10, x 1 ¼ 5, x 2 ¼ 4, x 3 ¼ 1, and p 1 ¼ 0.6, p 2 ¼ 0.3, and p 3 ¼ 0.1
10! 5 4 1
The probability is ð0:6Þ ð0:3Þ ð0:1Þ ¼ 1260ð0:000062986Þ¼
5!4!1!
0.07936