Dec 17, 2016

# Probability — practice test 4C

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

Directions:

• Provide an appropriate response.
• 1. When asked about the probability that he would become a sumo wrestler, Sam replied “slim to none”. Relate that phrase to a numeric probability and interpret his meaning.

Sam is essentially saying: P(sumo wrestler) = 0, will not ever occur.

1. 2. If a game were “fair”, the payoff on a bet would be the same as the odds for the event. In one game, the odds for winning are 1:13. If the game were “fair”, what would the payoff be for a \$5 bet? Of course, games in casinos are designed to make a profit for the casino investors. Supposing the casino makes the payoff at 1:11 odds, what profit does the casino make on your winning bet?

If a “fair” game the payoff would be \$70 = 13 * 5 + 5 original bet. The casino payoff would be \$60 = 11 * 5 + 5 original bet. The profit would be \$10.

1. 3. Suppose that a class of 30 students is assigned to write an essay.
1) Suppose 4 essays are randomly chosen to appear on the class bulletin board. How many different groups of 4 are possible?
2) Suppose 4 essays are randomly chosen for awards of \$10, \$7, \$5, and \$3. How many different groups of 4 are possible?
Explain the significant differences between problems 1 and 2.

Problem 1 is a combination, not dependent on order, while problem 2 is a permutation and is dependent on order. 27,405 different groups of 4 are possible for problem 1; 657,720 different groups of 4 are possible for problem 2.

2. Express the indicated degree of likelihood as a probability value.
• 4. “There is a 40% chance of rain tomorrow.”
1. 0.40
2. 0.60
3. 40
4. 4

• 5. On a multiple-choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess?
1. ¾
2. ¼
3. ½
4. 1

4. Find the indicated probability.
• 6. Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 3?
1. 1/18
2. 1/2
3. 17/18
4. 2

5. Answer the question, considering an event to be “unusual” if its probability is less than or equal to 0.05.
• 7. Assume that one student in your class of 28 students is randomly selected to win prize. Would it be “unusual” for you to win?
1. Yes
2. No

• 8. The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least \$83,000. Round your answers to the nearest tenth.
89,000 95,000 75,000 98,000 79,000 89,000 83,000 67,000 104,000 119,000 71,000 86,000 101,000 79,000 95,000 92,000 83,000 107,000 63,000 92,000
1. 0.4
2. 0.6
3. 0.8
4. 0.7

• 9. Suppose you are playing a game of chance. If you bet \$5 on a certain event, you will collect \$200 (including your \$5 bet) if you win. Find the odds used for determining the payoff.
1. 200 : 205
2. 1 : 39
3. 39 : 1
4. 40 : 1

7. Find the indicated probability.
• 10. If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.
1. 31/365
2. 11/12
3. 31/334
4. 334/365

• 11. The table below describes the smoking habits of a group of asthma sufferers. If one of the 1033 people is randomly selected, find the probability that the person is a man or a heavy smoker.
1. 0.597
2. 0.563
3. 0.550
4. 0.502

• 12. A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
1. ¾
2. 4/3
3. 9
4. ¼

• 13. In a homicide case 7 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 7 witnesses would pick the same person.
1. 0.0000595
2. 0.0000128
3. 0.000064
4. 1.4

• 14. Among the contestants in a competition are 49 women and 29 men. If 5 winners are randomly selected, what is the probability that they are all men?
1. 0.00563
2. 0.06228
3. 0.09784
4. 0.07261

• 15. A study conducted at a certain college shows that 54% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
1. 0.111
2. 0.996
3. 0.540
4. 0.999

• 16. The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time given that it was an Upstate Airlines flight.
1. 43/87
2. 43/48
3. None of the above is correct.
4. 11/76

8. Solve the problem.
• 17. A firm uses trend projection and seasonal factors to simulate sales for a given time period. It assigns “0” if sales fall, “1” if sales are steady, “2” is sales rise moderately, and “3” if sales rise a lot. The simulator generates the following output.

0 1 0 2 2 0 0 1 2 0 2 0 2 0 2 2 1 2 0 1 2 2 2 0 3 0 0 2 1 2 1

Estimate the probability that sales will remain steady.
1. 0.194
2. 0.125
3. 0.258
4. 0.412

• 18. There are 9 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?
1. 59,049
2. 126
3. 15,120
4. 120

• 19. A pollster wants to minimize the effect the order of the questions has on a person’s response to a survey. How many different surveys are required to cover all possible arrangements if there are 8 questions on the survey?
1. 64
2. 5040
3. 8
4. 40,320

• 20. A class has 8 students who are to be assigned seating by lot. What is the probability that the students will be arranged in order from shortest to tallest? (Assume that no two students are the same height.)
1. 0.00019841
2. 0.1000
3. 0.00024802
4. 0.0000248