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Name: __________________________ Date: _____________
1. A die is rolled and a coin is flipped simultaneously. The number rolled on the die and
whether the coin lands heads or tails is recorded. How many outcomes are in the
sample space?
A) 8
B) 6
C) 10
D) 12
2. A spinner numbered 1 through 10 is spun and one die is tossed simultaneously. The
number spun and the number rolled are recorded. How many outcomes are in the
sample space?
A) 60
B) 16
C) 10
D) 6
3. Three dice are tossed. The number rolled on each die is recorded. How many
outcomes are in the sample space?
A) 18
B) 72
C) 216
D) 42
4. Three dice are rolled and the sum of the numbers rolled is recorded. The outcomes in
the sample space are all equally likely.
A) True
B) False
5. There are seven blue and six black socks in a drawer. One is pulled out at random.
Find the probability that it is black.
A) 6/13
B) 6/7
C) 1/2
D) 1/6
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6. A fair coin is tossed three times. Find the probability of getting exactly 2 heads.
A) 1/2
B) 1/3
C) 2/3
D) 3/8
7. A computer is programmed to randomly print two letters in a row without repeating a
letter. What is the probability that the first combination printed is the word "DO"?
A) 1/650
B) 1/325
C) 2/325
D) 1/26
8. A computer system requires users to have an access code that consists of a three-digit
number that is not allowed to start with zero and cannot repeat digits. How many such
codes are possible?
A) 990
B) 648
C) 729
D) 720
9. A sample space has three outcomes, A, B, and C. The probability of outcome A is 0.39
and the probability of outcome B is 0.25. What is the probability of outcome C?
A) 0.36
B) 0.33
C) 0.5
D) 0.64
10. A raffle ticket costs $5. First and second prize winners will be drawn at random. The
probability of winning the $100 first prize is 1/40 and the probability of winning the $25
second prize is 1/20. What is the mean winnings for one play, taking into account the
$5 cost of the ticket?
A) –1.25
B) –0.875
C) 3.375
D) 3.75
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11. At a certain discount store, the number of people in checkout lines varies. The
probability model for the number of people in a randomly chosen line is:
Number in line
Probability
0
0.08
1
0.15
2
0.20
3
0.22
4
0.15
5
0.20
What is the mean number of people in a line?
A) 2.5
B) 15.92
C) 2.81
D) 2.89
12. The shelf life of a battery produced by one major company is known to be normally
distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What
is the upper quartile of battery shelf life?
A) 4.0025 years
B) 4.25 years
C) 4.17 years
D) 5.25 years
13. The mean length of time, per week, that students at a certain school spend on their
homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the
distribution of study times is normal, what percent of students spend more than 25.238
hours per week on homework?
A) 16.5%
B) 5%
C) 12.5%
D) 25%
14. The scores of students on a standardized test are normally distributed with a mean of
300 and a standard deviation of 40. Between what two values do 99.7% of the test
scores lie?
A) 260 to 340
B) 220 to 380
C) 297 to 303
D) 180 to 420
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15. The shelf life of a battery produced by one major company is known to be normally
distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What
percent of batteries last between 1.25 and 5.75 years?
A) 99.7%
B) 95%
C) 68%
D) 50%
16. The weight of bags of potato chips produced by one machine at a packaging plant has a
standard deviation of 0.2 ounces. Suppose a sample of 25 bags is drawn from a
production run and weighed. What is the standard deviation x of the mean result?
A) 0.008
B) 0.04
C) 0.2
D) 1.0
17. A poll of 60 students found that 20% were in favor of raising parking fees to pave two
new parking lots. The standard deviation of this poll is about 5.2%. What would be
the standard deviation if the sample size was increased from 60 students to 120
students?
A) 10.4%
B) 7.3%
C) 2.6%
D) 3.68%
18. A game is played with a pair of tetrahedral (four-sided) dice. Each die has faces
numbered 1, 2, 3, and 4. To play, roll the two dice and record the sum of the values on
the down faces. What is the probability of rolling a sum of 6?
A) 1/2
B) 1/8
C) 3/8
D) 3/16
19. A spinner with regions numbered 1 to 4 is spun and a coin is tossed. Both the number
spun and whether the coin lands heads or tails is recorded. Write the sample space.
20. A pair of dice is rolled. Sam says there are 36 outcomes in the sample space for this
procedure and Sally says there are 11 outcomes in the sample space. Explain how they
could both be correct.
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21. If the probability that Kerry gets an “A” in English class is 0.82, what is the probability
that Kerry does not get an "A?"
22. Find the probability of drawing a three or a heart from a regular (bridge) deck of cards.
(Such a deck consists of four suits of thirteen cards each. The suits are hearts, spades,
diamonds, and clubs. The cards are 1 through 10, Jack, Queen, and King.)
23. A license plate code consists of two letters followed by three digits. The letters cannot
repeat, but the digits can. What is the probability that a randomly chosen plate has all
three digits the same?
24. Suppose a game has four outcomes, A, B, C, and D. The probability of outcome A is
0.4, the probabilities of each of the other outcomes is 0.2. A player receives $2 if
outcome A occurs, $3 if outcome B occurs, $1 if outcome C occurs, and must pay $5 if
outcome D occurs. What is the mean value of one trial of this game?
25. Suppose a trial consists of rolling a single die and reporting the number that is rolled.
What are the possible outcomes? Are they equally likely?
26. In the manufacturing process for ball bearings, the mean diameter is 5 mm with a
standard deviation of 0.002 mm. Between what two measurements will 95% of all
diameters of ball bearings be found?
27. In the manufacturing process for ball bearings, the mean diameter is 5 mm with a
standard deviation of 0.002 mm. Each hour a sample of 20 bearings is drawn,
measured, and the mean diameter of the sample found. What is the standard deviation
x of the sample mean?
28. A game consists of tossing a coin and rolling a six-sided die. The results can be
recorded easily; for example, if heads shows on the coin and a 4 shows on the die,
record this as H4. List the sample space for the results of this game.
29. Suppose you use a spinner to choose a random number between 0 and 1. Which is
more likely—choosing a number between 1/3 and 2/3, or between 1/2 and 3/4?
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30. According to the central limit theorem, how does the standard deviation of averages
over four observations compare to the standard deviation of individual observations?
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Answer Key
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{(1,H), (2,H), (3,H), (4,H), (1,T), (2,T), (3,T), (4,T)}
Sam counts 36 outcomes in the sample space by observing the number rolled on each
die. Sally counts 11 outcomes by observing the sum rolled on the die.
The probability Kerry does not get an “A” is 0.18.
The probability of drawing a three or a heart is 16/52 or 0.308.
6500/650,000 = 1/100 = 0.01
The mean value of one trial is $0.60.
Possible outcomes are 1, 2, 3, 4, 5, 6. They are equally likely.
95% of all diameters will be between 4.996 and 5.004 mm.
0.000447
H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6
Choosing a number between 1/3 and 2/3
The standard deviation of the averages is half that of the individual observations.
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