Chapter 4 Probability and Counting Rules

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Chapter 4 Probability and Counting Rules. Section 4-4. The Multiplication Rules and Conditional Probability. Chapter 4 Probability and Counting Rules. Section 4-4. Exercise #7. Section 4-4 Exercise #7.

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Chapter 4 Probability and Counting Rules

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Chapter 4

Probability and Counting Rules

Section 4-4

The Multiplication Rules and Conditional Probability

Chapter 4

Probability and Counting Rules

Section 4-4

Exercise #7

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.

• None have computers
• At least one has a computer
• All have computers

None have computers

• At least one has a computer
• All have computers

Section 4-4 Exercise #31

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.

Section 4-4 Exercise #35

Consider this table concerning utility

patents granted for a specific year.

• Select one patent at random.
• What is the probability that it is a
• foreign patent, given that it was
• issued to a corporation?
• What is the probability that it

was issued to an individual,

given that it was a U.S. patent?

What is the probability that it is a

• foreign patent, given that it was
• issued to a corporation?

What is the probability that it was

issued to an individual, given that

it was a U.S. patent?

Chapter 4

Probability and Counting Rules

Section 4-5

Counting Rules

Section 4-5 Exercise #9

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?

Section 4-5 Exercise #21

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?

Section 4-5 Exercise #31

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

Section 4-5 Exercise #41

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

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

Chapter 4

Probability and Counting Rules

Section 4-6

Probability and Counting Rules

Section 4-6 Exercise #3

In a company there are 7 executives: 4 women and 3 men. Three are selected to attend a management seminar. Find these probabilities.

• All 3 selected will be women.
• All 3 selected will be men.
• c. 2 men and 1 woman will be selected.
• d. 1 man and 2 women will be selected.

All 3 selected will be women.

• All 3 selected will be men.

c. 2 men and 1 woman will be selected.

d. 1 man and 2 women will be selected.

Section 4-6 Exercise #9

A committee of 4 people is to be formed from 6 doctors and 8 dentists. Find the probability that the committee will consist of:

• All dentists.
• b. 2 dentists and 2 doctors.
• c. All doctors.
• d. 3 doctors and 1 dentist.
• e. 1 doctor and 3 dentists.

All dentists.

• 2 dentists and 2 doctors.
• All doctors.

3 doctors and 1 dentist.

• e. 1 doctor and 3 dentists.

Section 4-6 Exercise #11

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

• What is the probability that you get a pair of red socks?
• What is the probability that you get a pair of black socks?
• What is the probability that you get 2 unmatched socks?
• Where did the other red sock go?

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

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

Chapter 4

Probability and Counting Rules

Section 4-6

Exercise #15

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.