Dec 14, 2016

# Probability — practice test 4B

20 cards
Problems with solutions in Elementary Statistics — Probability Fundamentals, Addition and Multiplication Rules, Counting, Bayes’ Theorem

Directions:

• Provide an appropriate response.
• 1. Describe an event whose probability of occurring is 1 and explain what that probability means. Describe and event whose probability of occurring is 0 and explain what that probability means.

Answers will vary. Answers should include: Probability = 1, anything that is a sure thing, must occur. Probability = 0, anything that will never occur.

1. 2. Under what circumstances can you sample without replacement and still use the multiplication rule for independence? Discuss population and sample size as you answer this question.

The sample size must be no more than 5% of the population size. So, taking something very small out of something very large will effectively result in essentially the same probability value for sampling without replacement as that for sampling with replacement, which is an easier formula to use.

1. 3. Consider the following formulas:

Given the same values for n and r in each formula, which is the smaller value, P or C?
How does this relate to the concept of counting the number of outcomes based on whether or not order is a criterion?

The combination value will be smaller, since order is not important. For example, ABC is equivalent to ACB and would not be counted twice. If, however, r is 0 or 1 then nPr = nCr.

2. Express the indicated degree of likelihood as a probability value.
• 4. “You have a 50-50 chance of choosing the correct answer.”
1. 50
2. 0.25
3. 0.50
4. 0.9

• 5. Which of the following cannot be a probability?
1. 2/3
2. ½
3. 3/5
4. 5/3

4. Find the indicated probability.
• 6. In a poll, respondents were asked whether they had ever been in a car accident. 471 respondents indicated that they had been in a car accident and 420 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth, if necessary.
1. 1.121
2. 0.529
3. 0.002
4. 0.471

5. Answer the question, considering an event to be “unusual” if its probability is less than or equal to 0.05.
• 7. Is it “unusual” to get a 12 when a pair of dice is rolled?
1. Yes
2. No

• 8. Of 1275 people who came into a blood bank to give blood, 278 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.
1. 0.186
2. 0.269
3. 0.218
4. 0.137

• 9. Find the odds against correctly guessing the answer to a multiple-choice question with 6 possible answers.
1. 6 : 1
2. 5 : 6
3. 5 : 1
4. 6 : 5

7. Find the indicated probability.
• 10. The probability that Luis will pass his statistics test is 0.65. Find the probability that he will fail his statistics test.
1. 0.33
2. 0.35
3. 1.86
4. 1.54

• 11. A study of consumer smoking habits includes 161 people in the 18-22 age bracket (50 of whom smoke), 144 people in the 23-30 age bracket (35 of whom smoke), and 80 people in the 31-40 age bracket (28 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.
0.091
1. 0.577
2. 0.668
3. 0.243

• 12. 100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of 100 employees is randomly selected, find the probability that the person drives alone or cycles to work.

1. Public transportation: 8 full time, 9 part time.
2. Bicycle: 3 full time, 3 part time.
3. Drive alone: 28 full time, 31 part time.
4. Carpool: 9 full time, 9 part time.
1. 0.65
2. 0.36
3. 0.59
4. 0.31

• 13. A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.
1. 0.027
2. 0.429
3. 0.343
4. 2.1

• 14. A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected are defective?
1. 0.1627
2. 0.1550
3. 0.1089
4. 10. 1632

• 15. In a batch of 8,000 clock radios 6% are defective. A sample of 5 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected?
1. 0.0600
2. 0.200
3. 0.266
4. 0.734

• 16. The table below describes the smoking habits of a group of asthma sufferers.

If one of the 962 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is a light smoker.
1. 0.272
2. 0.093
3. 0.539
4. 0.185

8. Solve the problem.
• 17. Swinging Sammy Skor’s batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let 1 = HIT and 0 = OUT. The output from the simulation was as follows.

1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1

Estimate the probability that he gets a hit.
1. 0.452
2. 0.286
3. 0.476
4. 0.301

• 18. How many ways can an IRS auditor select 4 of 13 tax returns for an audit?
1. 24
2. 28,561
3. 715
4. 17,160

• 19. A tourist in France wants to visit 8 different cities. How many different routes are possible?
1. 40,320
2. 5040
3. 64
4. 8

• 20. In a certain lottery, five different numbers between 1 and 36 inclusive are drawn. These are the winning numbers. To win the lottery, a person must select the correct 5 numbers in the same order in which they were drawn. What is the probability of winning?
1. 1/45,239,040
2. 1/120
3. 1/36!
4. 120/45,239,040