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

2. Probability and Counting Rules
Chapter 4
Probability and Counting Rules
Section 4-4
Exercise #7

3. At least one has a computer All have computers
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

4. None have computers
At least one has a computer
All have computers

5. Section 4-4 Exercise #21

7. In Rolling Acres Housing Plan, 42% of the houses have
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.

8. Consider this table concerning utility
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?

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

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

13. Probability and Counting Rules
Chapter 4
Probability and Counting Rules
Section 4-5
Counting Rules

14. 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?

15. 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?

16. Section 4-5 Exercise #31
How many ways can a committee of 4 people be selected from a group of 10 people?

17. How many ways can a foursome of 2 men and 2 women
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?

18. Probability and Counting Rules
Chapter 4
Probability and Counting Rules
Section 4-6
Probability and Counting Rules

19. All 3 selected will be women. All 3 selected will be men.
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.

20. All 3 selected will be women.
All 3 selected will be men.

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

22. 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.

23. All dentists.
2 dentists and 2 doctors.
All doctors.

24. 3 doctors and 1 dentist.
e. 1 doctor and 3 dentists.

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

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

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

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

29. 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.