Chapter 5 Review Exercises

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.

Question 5.411

1. 2 heads

5.99.1

3/8

Question 5.412

2. At least 2 heads

Question 5.413

3. 4 heads

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0

Question 5.414

4. 2 tails

Question 5.415

5. At most 1 tail

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1/2

Question 5.416

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

  1. What is the probability that the sonnet is by Shakespeare?
  2. What method of assigning probability do you think was used here? Why was this method used, and not the others?

section 5.2

Question 5.417

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:

  1. The probability that a noncitizen farmworker is a high school graduate or has some college
  2. The probability that a citizen farmworker is a high school graduate or has some college
  3. The probability that a noncitizen farmworker has less than a ninth-grade education and has some college
  4. The probability that a farmworker is not a citizen
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

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(a) 0.213 (b) 0.656 (c) 0 (d) 0.376

section 5.3

Question 5.418

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:

  1. Three randomly selected research studies all favor this drug.
  2. None of the three randomly selected research studies favors this drug.
  3. At least one of three randomly selected research studies favors this drug.

Question 5.419

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.

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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

Question 5.420

10. Find the probability that a randomly chosen person has the following characteristics:

  1. Owns a cat,
  2. Owns a dog,

Question 5.421

11. Find the probability that a randomly chosen person has the following characteristics:

  1. Is female and owns a dog,
  2. Is male and owns a dog,

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(a) 1/6 (b) 1/6

Question 5.422

12. Find the following conditional probabilities for a randomly chosen person:

  1. Owns a dog, given that the person is female,
  2. Owns a dog, given that the person is male,

Question 5.423

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.

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Men's TV channel, since

section 5.4

Question 5.424

14. How many distinguishable strings of letters can be made using all the letters in the word MISSISSIPPI?

Question 5.425

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?

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60

Question 5.426

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.

  1. Explain whether the drill instructor is using a permutation or a combination.
  2. Find the number of ways that both soldiers will fail the inspection.
  3. Find the probability that the entire squad will have to run a five-mile course in full gear.