Name:
Date: 2023/10/18
AP Statistics
Chapter 5 Review Test
AP Multiple Choice: Identify the choice that best completes the statement or answers the question
1. Suppose that, in a certain part of the world, in any
50-year period the probability of a major plague is
0.39, the probability of a major famine is 0.52, and
the probability of both a plague and a famine is
0.15. What is the probability of a famine given that
there is a plague?
a.
b.
c.
d.
e.
5. A city water supply system involves three pumps,
the failure of any one of which crashes the system.
The probabilities of failure for each pump in a
given year are 0.025, 0.034, and 0.02, respectively.
Assuming the pumps operate independently of
each other, what is the probability that the system
does not crash during the year?
0.240
0.288
0.370
0.385
0.760
a.
b.
c.
d.
e.
Use the following for #2-3. Consider the following
table of ages of U.S. Senators:
Age(yr.) < 40
Number of
5
Senators
40 – 49
50 – 59
60 – 69
30
36
22
70 – 79 > 79
5
2. What is the probability that a senator is above 49
years old?
a.
b.
c.
d.
e.
0.55
0.65
0.35
0.95
0.05
3. What is the probability that a senator is under 70
years old given that he or she is at least 50 years
old?
a.
b.
c.
d.
e.
0.580
0.624
0.643
0.892
0.969
4. If P(A) = 0.2 and P(B) = 0.1, what is P(A υ B) if A
and B are mutually exclusive?
a.
b.
c.
d.
e.
0.02
0.28
0.30
0.32
There is insufficient information to
answer this question.
2
Less than 0.05
0.077
0.79
0.081
0.923
6. The probability that a randomly chosen American
is a Republican is 0.35. What is the probability
that in a sample of 10 Americans, that at least one
will be a Republican?
a.
b.
c.
d.
e.
0.9865
0.2275
0.0725
0.0135
0.0072
7. The probability that you will be ticketed for
illegal parking on campus is about 1/3. During
the last nine days, you have illegally parked every
day and have NOT been ticketed (you lucky
person!). Today, on the 10th day, you again
decide to park illegally. Assuming the outcomes
are independent from day to day, the probability
that you will be caught is
a.
b.
c.
d.
e.
!
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+ ""#
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#
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8. Of people who died in the United States in a recent
year, 86% were white, 12% were black, and 2%
were Asian. (We will ignore the small number of
deaths among other races.) Diabetes caused 2.8%
of deaths among whites, 4.4% among blacks, and
3.5% among Asians. The probability that a
randomly chosen death was due to diabetes is
about
a.
b.
c.
d.
e.
0.96
0.107
0.042
0.038
0.030
9. A friend has placed a large number of plastic
disks in a hat and invited you to select one at
random. He informs you that they have numbers
on them and that one of the following is the
probability model for the number on the disk you
have chosen. Which one is it
a.
b.
c.
10.
11.
12.
13.
d.
11. The conditional probability of A, given B
a.
b.
c.
d.
e.
Is ½
Is 3/10
Is 1/5
Is 1/6
Cannot be determined from the information
given.
12. We may conclude that
a.
b.
c.
d.
e.
Events A and B are independent.
Events A and B are mutually exclusive.
Either A or B always occurs.
Events A and B are complementary.
None of the above is correct
13. A poker player is dealt poor hands for several
hours. He decides to bet heavily on the last hand of the
evening on the grounds that after many bad hands, he
is due for a winner.
a. He's right because the winnings have to average out.
b. He's wrong, because successive deals are
independent of each other
c. He's right, because successive deals are
independent of each other.
d. He's wrong, because he’s clearly on a “cold streak.”
e. Whether he’s right or wrong depends on how many
bad hands he’s been dealt so far.
e.
Use the following for #14-15. The two-way table
below gives information on seniors and juniors at a
high school and by which means they typically get to
school.
10. You draw two marbles at random from a jar that
has 20 red marbles and 30 black marbles without
replacement. What is the probability that both
marbles are red?
a.
b.
c.
d.
e.
0.1551
0.1600
0.2222
0.4444
0.8000
Use the following for #11-12. An event A will occur
with a probability 0.5. An event B will occur with
probability 0.6. The probability that both A and B will
occur is 0.1.
14. You select one student from this group at
random. What is the probability that this student
typically takes a bus to school?
a.
b.
c.
d.
e.
0.256
0.309
0.353
0.455
0.604
15. You select one student from this group at random.
If the student says he is a junior, what is the
probability that he walks to school?
a.
b.
c.
d.
e.
0.073
0.160
0.455
0.600
0.833
1
2
3
4
5
6
7
9
10
11
12
13
14
15
8
Determine whether each of the following simulation designs is valid. Justify your answer.
16. A tennis player gets 95% of his serves in play during practice. To simulate the player hitting 5 serves, look at
5 pairs of digits going across a row in Table D. If the number is between 00 and 94, the serve is in; numbers
between 95 and 99 indicate that the serve is out.
17. One person is randomly chosen from a group of 10 females and 50 males. Use a 6-sided die. Let 1 represent a
female and 2-6 represent a male. Roll the die to determine if the person chosen was male or female.
For the following, answer the question by running a simulation of 20 trials for each problem. You may use
the random number generator on your calculator to run the simulations. Use the 4 step process.
18. A basketball player’s shooting percentage is about 1/3, or 33.3%. In one game, he misses all of the 12 shots
that he takes. Should he be surprised?
19. Researchers recruited 20 volunteers-8 men and 12 women-to take part in an experiment. They randomly
assigned the subjects into two groups of 10 people each. To their surprise, 6 of the 8 men were randomly
assigned to the same treatment. Should they be surprised?
20. A diagnostic test administered to detect the presence of HIV antibodies in the blood returns a positive result in
99.85% of those whose blood actually have the antibody. It also gives a false positive result for those who don’t
have the antibody 0.6% of the time. Define A as the event that a person actually has HIV antibodies present in
their blood and define P as the event that the test returns a positive result. If 1% of the population has HIV antibodies
present in their blood, then what is the probability that a patient whose test came back positive really does have
HIV antibodies present? Examine this question using each of the following approaches.
a. Notation/Probability Rules
b. Complete the table:
Test Results
Positive
HIV present
No HIV
Total
c. Draw a Venn Diagram
d. Draw a tree diagram
Negative
Total