Chapter 4 Probability and Counting Rules

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

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

3. 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. 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. 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?

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

19. 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. 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. 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.