Probability and Counting Rules

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

1. None have computers
2. At least one has a computer
3. All have computers

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1. None have computers
2. At least one has a computer
3. All have computers

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Section 4-4 Exercise 21
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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.
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Section 4-4 Exercise 35
Corporation Government Individual
U.S. 70,894 921 6129
Foreign 63,182 104 6267
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?

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

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

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Chapter 4 Probability and Counting Rules
Section 4-5
Counting Rules
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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?
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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?
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Section 4-5 Exercise 31
How many ways can a committee of 4 people be
selected from a group of 10 people?
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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?
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Chapter 4 Probability and Counting Rules
Section 4-6
Probability and Counting Rules
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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.

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1. All 3 selected will be women.

1. All 3 selected will be men.

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

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• All dentists.
• 2 dentists and 2 doctors.
• All doctors.

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• 3 doctors and 1 dentist.
• e. 1 doctor and 3 dentists.

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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.

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

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

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• c. What is the probability that you get 2
  unmatched socks?
• d. Where did the other red sock go?

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Chapter 4 Probability and Counting Rules
Section 4-6
Exercise 15
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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.