Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below.
Outcome
Probability
A) 3/14
A
1/14
B
1/14
B) 11/14
C
1/14
D
.
C) 1/14 D) 1/4
1)
2) An unusual event is an event that has a
A) Probability of 1
C) A negative probability
B) Probability which exceeds 1
D) Low probability of occurrence
3) The table below represents a random sample of the number of deaths per 100 cases for a certain illness over time. If a person infected with this illness is randomly selected from all infected people, find the probability that the person lives 3 4 years after diagnosis. Express your answer as a simplified fraction and as a decimal.
Years after Diagnosis Number deaths
1 2
3
5
7
9
-
-
-
-
11
13
15
4
6
8
10
-
-
+
12
14
15
35
6
4
16
9
2
13
; 0.35
; 0.058
; 0.538
; 0.029
2)
3)
4) In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The P(Red) =
18
38
0.47. This is an example of what type of probability?
A) Subjective B) Empirical C) Simulated D) Classical
5) In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. We watched a friend play roulette for two hours. In that time we noted that the wheel was spun 50 times and that out of those 50 spins black came up 22 times. Based on this data, the P(black ) =
22
50
= 0.44. This is an example of what type of probability?
A) Observational B) Empirical C) Subjective D) Classical
6) Classify the statement as an example of classical probability, empirical probability, or subjective probability. It is known that the probability of hitting a pothole while driving on a certain road is
1%.
A) subjective probability B) empirical probability C) classical probability
4)
5)
6)
1

7) How many ways can five people, A, B, C, D, and E, sit in a row at a concert hall if D and E will not sit next to each other?
A) 48 B) 72 C) 24 D) 60
8) The Environmental Protection Agency must inspect nine factories for complaints of water pollution. In how many different ways can a representative visit five of these to investigate this week?
A) 5 B) 15,120 C) 362,880 D) 45
9) A physics exam consists of 9 multiple choice questions and 6 open ended problems in which all work must be shown. If an examinee must answer 5 of the multiple choice questions and 4 of the open ended problems, in how many ways can the questions and problems be chosen?
A) 1890 B) 1080 C) 5,443,200 D) 261,273,600
10) A club elects a president, vice president, and secretary treasurer. How many sets of officers are possible if there are 13 members and any member can be elected to each position? No person can hold more than one office.
A) 17,160 B) 1716 C) 572 D) 858
11) In how many ways can a committee of three men and four women be formed from a group of 9 men and 9 women?
A) 5040 B) 1,524,096 C) 42 D) 10584
Solve the problem.
12) Given that P(A or B) =
1
4
, P(A) =
1
6
, and P(A and B) =
1
7
, find P(B). Express the probability as a simplified fraction.
A)
19
84
B)
17
168
C)
23
84
D)
47
84
7)
8)
9)
10)
11)
12)
13) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the probability of getting someone who is a man or a non drinker. Round your answer to three decimal places.
Sex
Man
Woman
Total
A) 0.831
Non drinker Regular Drinker Heavy Drinker Total
135
187
322
B) 0.947
47
21
68
5
7
12
C) 0.941
187
215
402
D) 0.930
13)
14) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is a queen or a club. Express the probability as a simplified fraction.
14)
15) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a ten, a king or a diamond. Round to the nearest hundredth.
A) 0.29
B) 0.31
C) 0.37
D) 0.40
15)
2

16) Two dice are rolled. What is the probability of having both faces the same (doubles) or a total of 4 or 10? Round to the nearest hundredth.
A) 0.28
B) 0.06
C) 0.15
D) 0.33
17) A game has three outcomes. The probability of a win is 0.4, the probability of tie is 0.5, and the probability of a loss is 0.1. What is the probability of not winning in a single play of the game.
A) 0.1
B) 0.33
C) 0.6
D) 0.5
Provide an appropriate response. Express your answer as a simplified fraction unless otherwise noted.
18) Numbered disks are placed in a box and one disk is selected at random. If there are 3 red disks numbered 1 through 3, and 2 yellow disks numbered 4 through 5, find the probability of selecting a disk numbered 3, given that a red disk is selected.
A)
2
5
B)
3
5
16)
17)
18)
19) Assume that P(A) = 0.7 and P(B) = 0.2. If A and B are independent, find P(A and B).
A) 1.00
B) 0.90
C) 0.76
D) 0.14
20) If P(A) = 0.72, P(B) = 0.11, and A and B are independent, find P(A|B).
A) 0.83
B) 0.0792
C) 0.11
D) 0.72
Provide an appropriate response.
21) A quiz consists of 100 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?
A) 5 B) 7.07106781
C) 2 D) 0
22) The probability that a house in an urban area will develop a leak is 5%. If 20 houses are randomly selected, what is the mean of the number of houses that developed leaks?
A) 0.5
B) 1.5
C) 1 D) 2
19)
20)
21)
22)
23) In a recent survey, 60% of the community favored building a health center in their neighborhood. If
14 citizens are chosen, find the probability that exactly 5 of them favor the building of the health center.
A) 0.357
B) 0.207
C) 0.041
D) 0.600
23)
24) 24) According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum?
A) 0.800
B) 0.200
C) 0.002
D) 0.820
25) The probability that a house in an urban area will develop a leak is 6%. If 87 houses are randomly selected, what is the probability that none of the houses will develop a leak?
A) 0.001
B) 0.060
C) 0.005
D) 0.000
25)
26) A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz?
A) 0.205
B) 0.006
C) 0.060
D) 0.377
26)
3

27) In a carnival game, a person wagers $2 on the roll of two dice. If the total of the two dice is 2, 3, 4,
5, or 6 then the person gets $4 (the $2 wager and $2 winnings). If the total of the two dice is 8, 9, 10,
11, or 12 then the person gets nothing (loses $2). If the total of the two dice is 7, the person gets
$0.75 back (loses $0.25). What is the expected value of playing the game once?
A) $0.42
B) $2.00
C) $0.00
D) $0.04
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28) Identify the sample space of the probability experiment: determining the puppie's gender for a litter of three puppies (Use M for male and F for female.)
28)
27)
29) Identify the sample space of the probability experiment: answering a multiple choice question with A, B, C, D and E as the possible answers
29)
30) The random variable x represents the number of boys in a family of three children.
Assuming that boys and girls are equally likely, (a) construct a probability distribution, and (b) graph the probability distribution.
30)
4

9) A
10) B
11) D
12) A
13) D
14) C
15) C
16) A
1) B
2) D
3) A
4) D
5) B
6) B
7) B
8) B
17) C
18) C
19) D
20) D
21) A
22) C
23) C
24) D
25) C
26) B
27) D
28) (MMM), (MMF), (MFM), (FMM), (MFF), (FMF), (FFM), (FFF)
29) (A, B, C, D, E)
5

30) (a) x P(x)
(b)
6