Chapter 4 Probability and Counting Rules Section 4-4 The Multiplication Rules and Conditional Probability.

Chapter 4Probability and Counting Rules

Section 4-4

The Multiplication Rules and Conditional Probability


Section 4-4

Exercise #7

At a local university 54.3% of incoming first-year students have computers. If three students are selected at random, find the following probabilities.a. None have computersb. At least one has a computerc. All have computers

Section 4-4 Exercise #7

a. None have computers

b. At least one has a computer

c. All have computers

A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I and 18% of its model II. If a model is selected at random, find the probability that it will be defective.


In Rolling Acres Housing Plan, 42% of the houses have a deck and a garage; 60% have a deck. Find the probability that a home has a garage, given that it has a deck.


Consider this table concerning utility patents granted for a specific year.Select one patent at random.a. What is the probability that it is a foreign patent, given that it was issued to a corporation?b. What is the probability that it was issued to an individual, given that it was a U.S. patent?

Corporation Government Individual

U.S. 70,894 921 6129

Foreign 63,182 104 6267


a. What is the probability that it is a foreign patent, given that it was issued to a corporation?

b. What is the probability that it was issued to an individual, given that it was a U.S. patent?


Section 4-5

Counting Rules

How many different 3 - digit identification tags can be made if the digits can be used more than once? If the first digit must be a 5 and repetitions are not permitted?


How many different ID cards can be made if there are 6 digits on a card and no digit can be used more than once?


How many ways can a committee of 4 people be selected from a group of 10 people?


How many ways can a foursome of 2 men and 2 women

be selected from 10 men and 12 women in a golf club?



Section 4-6

Probability and Counting Rules

In a company there are 7 executives: 4 women and 3 men. Three are selected to attend a management seminar. Find these probabilities.a. All 3 selected will be women.b. All 3 selected will be men.c. 2 men and 1 woman will be selected.d. 1 man and 2 women will be selected.


a. All 3 selected will be women.

b. All 3 selected will be men.

c. 2 men and 1 woman will be selected.

d. 1 man and 2 women will be selected.

A committee of 4 people is to be formed from 6 doctors and 8 dentists. Find the probability that the committee will consist of:a. All dentists.b. 2 dentists and 2 doctors.c. All doctors.d. 3 doctors and 1 dentist.e. 1 doctor and 3 dentists.


a. All dentists.

b. 2 dentists and 2 doctors.

c. All doctors.

d. 3 doctors and 1 dentist.

e. 1 doctor and 3 dentists.

A drawer contains 11 identical red socks and 8 identical black socks. Suppose that you choose 2 socks at random in the dark.a. What is the probability that you

get a pair of red socks?

b. What is the probability that you get a pair of black socks?

c. What is the probability that you get 2 unmatched socks?

d. Where did the other red sock go?


a. What is the probability that you get a pair of red socks?

b. What is the probability that you get a pair of black socks?

c. What is the probability that you get 2 unmatched socks?

d. Where did the other red sock go?


Section 4-6

Exercise #15

Find the probability that if 5 different- sized washers are arranged in a row, they will be arranged in order of size.


Chapter 4 Probability and Counting Rules Section 4-4 The Multiplication Rules and Conditional Probability.

Documents