section 5.1
For Exercises 1–5, consider the experiment of tossing a fair coin three times and find the probabilities of the following events.
1. 2 heads
5.99.1
3/8
2. At least 2 heads
3. 4 heads
5.99.3
0
4. 2 tails
5. At most 1 tail
5.99.5
1/2
6. A New Sonnet. Literature researchers have unearthed a sonnet that they know to be by either William Shakespeare or Christopher Marlowe. The probability that the sonnet is by Marlowe is 25%.
306
section 5.2
7. Farmworkers' Educational Level. The U.S. Department of Agriculture reports on the demographics of hired farmworkers.15 An excerpt of the results is provided in the table, showing the percentage of noncitizen and citizen farmworkers who attained various educational levels. The educational levels are mutually exclusive. Find the following probabilities:
| Noncitizens | Citizens | |
|---|---|---|
| Less than 9th grade | 238,008 | 61,776 |
| 9th–12th grade (no diploma) | 57,904 | 152,880 |
| High school graduate | 59,784 | 222,144 |
| Some college | 20,304 | 187,200 |
5.99.7
(a) 0.213 (b) 0.656 (c) 0 (d) 0.376
section 5.3
8. Drug Research Studies. The Annals of Internal Medicine reported that 39 of the 40 research studies sponsored by a drug company had outcomes favoring a certain drug. Find the following probabilities, assuming independence:
9. Drug Research Studies. Use the information in Exercise 8. Suppose we sample two research studies without replacement. Find the probability that the second study does not favor this drug, given that the first study does not favor this drug.
5.99.9
0
Gender and Pet Preference. Do you think your gender affects what type of pet you own? For Exercises 10–13, use the following table, showing preferences for various pets by owner gender.
| Gender of owner | Cats | Dogs | Other pets | Total |
|---|---|---|---|---|
| Female | 100 | 50 | 30 | 180 |
| Male | 50 | 50 | 20 | 120 |
| Total | 150 | 100 | 50 | 300 |
10. Find the probability that a randomly chosen person has the following characteristics:
11. Find the probability that a randomly chosen person has the following characteristics:
5.99.11
(a) 1/6 (b) 1/6
12. Find the following conditional probabilities for a randomly chosen person:
13. If you were a dog-food manufacturer, would you advertise more on a men's TV channel or a women's TV channel? Why? Cite your evidence.
5.99.13
Men's TV channel, since
section 5.4
14. How many distinguishable strings of letters can be made using all the letters in the word MISSISSIPPI?
15. Statistics Quiz. On a statistics quiz, there are five true/false questions, four fill-in-the-blank questions, and three short-answer questions. How many different ways are there of taking this quiz?
5.99.15
60
16. Inspection Time. A U.S. Army drill instructor will perform inspection on 2 soldiers in a squad of 18 soldiers. If both soldiers fail the inspection because their rifles are not clean, the entire squad will have to run a five-mile course in full gear. Three of the 18 soldiers have rifles that are not clean.