Download TEST 6A

Practice Test 6
AP Statistics
Name:
Directions: Work on these sheets.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. The probability of any outcome of a random phenomenon is
(a) the precise degree of randomness present in the phenomenon.
(b) any number as long as it is between 0 and 1.
(c) either 0 or 1, depending on whether or not the phenomenon can actually occur or not.
(d) the proportion of a very long series of repetitions on which the outcome occurs.
(e) none of the above.
2. If you choose a card at random from a well-shuffled deck of 52 cards, what is the probability that
the card chosen is not a heart?
(a) 0.25
(b) 0.50
(c) 0.75
(d) 1
(e) None of the above
3. You play tennis regularly with a friend, and from past experience, you believe that the outcome of
each match is independent. For any given match you have a probability of 0.6 of winning. The
probability that you win the next two matches is
(a) 0.16.
(b) 0.36.
(c) 0.4.
(d) 0.6.
(e) 1.2.
4. A basketball player shoots 8 free throws during a game. The sample space for counting the
number she makes is
(a) S = any number between 0 and 1.
(b) S = whole numbers 0 to 8.
(c) S = all sequences of 8 hits or misses, like HMMHHHMH.
(d) S = {HMMMMMMM, MHMMMMMM, MMHMMMMM, MMMHMMMM,
MMMMHMMM, MMMMMHMM, MMMMMMHM, MMMMMMMH}
(e) None of the above. The answer is _______________________________________
5. In a table of random digits such as Table B, each digit is equally likely to be any of 0, 1, 2, 3, 4, 5,
6, 7, 8, or 9. What is the probability that a digit in the table is a 0?
(a) 1
(b) 0
(c) 1/9
(d) 9/10
(e) 1/10
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Test 6A
6. In a table of random digits such as Table B, each digit is equally likely to be any of 0, 1, 2, 3, 4,
5, 6, 7, 8, or 9. What is the probability that a digit in the table is 7 or greater?
(a) 3/9
(b) 2/10
(c) 3/10
(d) 4/10
(e) 7/10
7. Choose an American household at random and let X be the number of cars (including SUVs and
light trucks) they own. Here is the probability model if we ignore the few households that own
more than 5 cars:
Number of cars X
Probability
0
0.09
1
0.36
2
0.35
3
0.13
4
0.05
5
0.02
A housing company builds houses with two-car garages. What percent of households have more
cars than the garage can hold?
(a) 7%
(b) 13%
(c) 20%
(d) 45%
(e) 55%
8.
Which of the following is (are) true?
I. The sum of the probabilities in a probability distribution can be any number between 0 and 1.
II. The probability of the union of two events is the sum of the probabilities of those events.
III. The probability that an event happens is equal to 1 – (the probability that the event does not
happen).
(a) I and II only
(b) I and III only
(c) II and III only
(d) I, II, and III
(e) None of the above gives the complete set of true responses.
9. People with type O-negative blood are universal donors. That is, any patient can receive a
transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If
10 people appear at random to give blood, what is the probability that at least 1 of them is a
universal donor?
(a) 0.526
(b) 0.72
(c) 0.28
(d) 0
(e) 1
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Test 6A
10. If a peanut M&M is chosen at random, the chances of it being a particular color are shown in the
table below.
Color
Probability
Brown
0.3
Red
0.2
Yellow
0.2
Green
0.2
Orange
0.1
Blue
The probability of randomly drawing a blue peanut M&M is
(a) 0.1.
(b) 0.2.
(c) 0.3.
(d) 1.0.
(e) According to this distribution, it’s impossible to draw a blue peanut M&M.
11. An assignment of probabilities must obey which of the following?
(a) The probability of any event must be a number between 0 and 1, inclusive.
(b) The sum of the probabilities of all outcomes in the sample space must be exactly 1.
(c) The probability of an event is the sum of the outcomes in the sample space that make up the
event.
(d) All of the above.
(e) Only (a) and (b) are true.
12. A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed
1996 more times, how many heads are most likely to appear for these 1996 additional tosses?
(a) 996
(b) 998
(c) 1000
(d) 1996
(e) None of the above. The answer is __________________________.
13. A die is loaded so that the number 6 comes up three times as often as any other number. What is
the probability of rolling a 1 or a 6?
(a) 1/3
(b) 1/4
(c) 1/2
(d) 2/3
(e) None of the above. The answer is __________________________.
Questions 14 and 15 relate to the following: In a particular game, a fair die is tossed. If the number
of spots showing is either four or five, you win $1. If the number of spots showing is six, you win $4.
And if the number of spots showing is one, two, or three, you win nothing. You are going to play the
game twice.
14. The probability that you win $4 both times is
(a) 1/6.
(b) 1/3.
(c) 1/36.
(d) 1/4.
(e) 1/12.
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Test 6A
15. The probability that you win at least $1 both times is
(a) 1/2.
(b) 4/36.
(c) 1/36.
(d) 1/4.
(e) 3/4.
Here is the probability model for the blood type of a randomly chosen person in the United States:
Blood type
Probability
O
0.45
A
0.40
B
0.11
AB
?
Questions 16, 16, and 18 use this information.
16. The probability that a randomly chosen American has type AB blood must be
(a) any number between 0 and 1.
(b) 0.45.
(c) 0.4.
(d) 0.96.
(e) 0.04.
17. Maria has type B blood. She can safely receive blood transfusions from people with blood types
O and B. What is the probability that a randomly chosen American can donate blood to Maria?
(a) 0.11
(b) 0.44
(c) 0.45
(d) 0.51
(e) 0.56
18. What is the probability that a randomly chosen American does not have type O blood?
(a) 0.04
(b) 0.11
(c) 0.45
(d) 0.55
(e) 0.51
19. An instant lottery game gives you probability 0.02 of winning on any one play. Plays are
independent of each other. If you play 3 times, the probability that you win on none of your plays
is about
(a) 0.98.
(b) 0.94.
(c) 0.000008.
(d) 0.06.
(e) 0.96.
20. The probability that you win on one or more of your 3 plays of the game in the previous question
is about
(a) 0.06.
(b) 0.02.
(c) 0.999992.
(d) 0.04.
(e) 0.98.
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Test 6A
21. Of people who died in the United States in a recent year, 86% were white, 12% were black, and
2% were Asian. (This ignores a 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 is a white who died of diabetes is about
(a) 0.107.
(b) 0.030.
(c) 0.024.
(d) 0.86.
(e) 0.03784.
22. Using the information in the previous question, the probability that a randomly chosen death was
due to diabetes is about
(a) 0.107.
(b) 0.038.
(c) 0.024.
(d) 0.96.
(e) 0.030.
23. Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10%
of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose
that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person
crime. Then the probability of observing no positive reading if all suspects plead innocent and are
telling the truth is
(a) 0.409.
(b) 0.735.
(c) 0.00001.
(d) 0.591.
(e) 0.99999.
Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps.
24. If four cards are drawn from a standard deck of 52 playing cards and not replaced, find the
probability of getting at least one heart.
25. When two dice are rolled, find the probability of getting
(a) a sum greater than 9.
(b) a sum less than 4 or greater than 9.
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Test 6A
26. Suppose you are given a standard six-sided die and told that the die is “loaded” in such a way that
while the numbers 1, 3, 4, and 6 are equally likely to turn up, the numbers 2 and 5 are three times
as likely to turn up as any of the other numbers.
(a) The die is rolled once and the number turning up is observed. Use the information given
above to fill in the following table:
Outcome
Probability
1
2
3
4
5
6
(b) Let A be the event: the number rolled is a prime number (a number is prime if its only factors
are 1 and the number itself; note that 1 is not prime). List the outcomes in A and find P(A).
(c) Let B be the event: the number rolled is an even number. List the outcomes in B and find
P(B).
(d) Are events A and B disjoint? Explain briefly.
(e) Determine if events A and B are independent.
27. If three dice are rolled, find the probability of getting triples (that is, 1,1,1 or 2,2,2 or 3,3,3,
etc.).
28. A coin is tossed five times.
(a) Find the probability of getting at least one tail.
(b) Find the probability of getting exactly 4 tails.
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Test 6A
29. Many fire stations handle emergency calls for medical assistance as well as those requesting
firefighting equipment. A particular station says that the probability that an incoming call is for
medical assistance is 0.85. This can be expressed as P(call is for medical assistance) = 0.85.
(a) Give a relative frequency interpretation of the given problem.
(b) What is the probability that a call is not for medical assistance?
(c) Assuming that successive calls are independent of one another, calculate the probability that
two successive calls will both be for medical assistance.
(d) Still assuming independence, calculate the probability that for two successive calls, the first is
for medical assistance and the second is not for medical assistance.
(e) Still assuming independence, calculate the probability that exactly one of the next two calls
will be for medical assistance.
(f) Do you think that it is reasonable to assume that the requests made in successive calls are
independent? Explain briefly.
30. Suppose that for a group of consumers, the probability of eating pretzels is 0.75 and that the
probability of drinking Coke is 0.65. Further suppose that the probability of eating pretzels and
drinking Coke is 0.55. Determine if these two events are independent.
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Test 6A
31. Suppose there are 10 multiple choice questions on a quiz. Each question has three choices (a, b,
and c) for an answer. Unfortunately, you went to see a movie the night before, and you were
unprepared for the quiz. You decide to guess the correct answers by randomly choosing one of
the three choices. Describe a simulation to estimate the probability of answering at least 4 of the
ten questions correctly. Carry out 3 repetitions. That is, simulate taking the quiz 3 times.
Use the random digits table, starting at line 103 (reproduced below).
line 103:
45467
71709
77558
00095
32863
29485
82226
90056
line 104:
52711
38889
93074
60227
40011
85848
48767
52573
Address these steps:
• correspondence
• repetition
• stopping rule
• estimate probability
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Test 6A