Dec 14, 2016

# Probability — practice test 4A

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

Directions:

• Provide an appropriate response.
• 1. Probabilities are useful in the decision-making process. Suppose a random sample of 152 students was surveyed regarding an instructor’s teaching. Suppose 105 students rated the instructor either excellent or above average on lecture presentations, 96 students rated the instructor as giving difficult or very difficult assignments and tests. Would you take this instructor for a class? Discuss the influence of probabilities on making this decision.

Answers will vary. Ratios could be considered as relative frequency probabilities, such as P(I take the instructor). Answer could address P(good lecturer) = 0.691; P(difficult assessments) = 0.632.

1. 2. Give an example of events which are independent but not mutually exclusive.

Answers will vary, but might include something like eating steak for supper and losing your car keys.

1. 3. Suppose a student is taking a 5-response multiple choice exam; that is, the choices are A, B, C, D, and E, with only one of the responses correct. Describe the complement method for determining the probability of getting at least one of the questions correct on the 15-question exam. Why would the complement method be the method of choice for this problem?

P(at least one correct) = 1 – P(none are correct). The alternative to the complement method is to find P(1), P(2), …P(15) and take this sum. This method is too time consuming and too difficult.

2. Express the indicated degree of likelihood as a probability value.
• 4. “It will definitely turn dark tonight.”
1. 0.67
2. 0.30
3. 0.5
4. 1

• 5. Which of the following cannot be a probability?
1. 1
2. 0
3. –1
4. ½

4. Find the indicated probability.
• 6. A class consists of 13 women and 49 men. If a student is randomly selected, what is the probability that the student is a woman?
1. 1/62
2. 13/62
3. 13/49
4. 49/62

5. Answer the question, considering an event to be “unusual” if its probability is less than or equal to 0.05.
• 7. Assume that a study of 500 randomly selected schools bus routes showed that 483 arrived on time. Is it “unusual” for a school bus to arrive late?
1. No
2. Yes

• 8. A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 0 = FOR, 1 = AGAINST. If the referendum were held today, estimate the probability that it would pass.
0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0
1. 0.6
2. 0.5
3. 0.4
4. 0.65

• 9. In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly form the town, what are the odds against selecting someone who commutes by bicycle?
1. 1 : 3
2. 1 : 4
3. 3 : 1
4. 3 : 4

7. Find the indicated probability.
• 10. Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.230. Find the probability that in a given year it will not snow on January 1st in that town.
1. 4.348
2. 1.230
3. 0.770
4. 0.299

• 11. Of the 57 people who answered “yes” to a question, 8 were male. Of the 61 people that answered “no” to the question, 5 were male. If one person is selected at random from the group, what is the probability that the person answered “yes” or was male?
1. 0.525
2. 0.14
3. 0.11
4. 0.593

• If one of the 996 people is randomly selected, find the probability of getting a regular or heavy smoker.
1. 0.442
2. 0.216
3. 0.095
4. 0.146

• 13. In one town, 76% of adults have health insurance. What is the probability that 8 adult selected at random from the town all have health insurance?
1. 6.08
2. 0.76
3. 0.111
4. 0.105

• 14. A IRS auditor randomly selects 3 tax returns from 58 returns of which 8 contain errors. What is the probability that she selects none of those containing errors?
1. 0.6407
2. 0.0026
3. 0.0018
4. 0.6352

• 15. A sample of 4 different calculators is randomly selected from a group containing 17 that are defective and 36 that have ne defects. What is the probability that at least one of the calculators is defective?
1. 0.799
2. 0.787
3. 0.170
4. 0.201

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

If one of the 930 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that it is a woman. Round to the nearest thousandth.
1. 0.399
2. 0.688
3. 0.505
4. 0.343

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 2 = OUT. The output from the simulation was as follows.

1 2 2 2 1 2 2 2 2 2 1 1 2 2 2 2 2 1 1 1 2 2 2 2 2 1 1 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2

Estimate the probability that he makes an out.
1. 0.667
2. 0.621
3. 0.810
4. 0.782

• 18. The library is to be given 8 books as a gift. The books will be selected from a list of 20 titles. If each book selected must have a different title, how many possible selections are there?
1. 125,970
2. 6.033983155e+13
3. 5.0791104e+09
4. 2.432902008e+18

• 19. A musician plans to perform 4 selections. In how many ways can she arrange the musical selections?
1. 120
2. 24
3. 16
4. 4

• 20. A tourist in France wants to visit 10 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?
1. 1/10
2. 3,628,800
3. 1/ 3,628,800
4. 1/100