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AP Statistics
Chapter 6 Test - 80 points
Name: _____________________
Period: _____________________
PART I: Circle the letter corresponding to the best answer. If you are able to show some work, you can
earn some partial credit. (4 points each)
1. A randomly selected student is asked to respond to “yes”, “no”, or “maybe” to the question; “Do you
intend to vote in the next presidential election?”. The sample space is {yes, no, maybe}. Which of
the following represents a possible assignment of probabilities for this sample space?
A.
B.
C.
D.
E.
0.5, 0.7, -0.2
0.4, 0.6, 0.4
0.3, 0.3, 0.3
0.4, 0.4, 0.2
None of the above
2. If you choose a card at random from a well-shuffled deck of cards, what is the probability that the
card chosen is not a heart?
A.
B.
C.
D.
E.
1.00
0.75
0.50
0.25
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 proabability of 0.6 of winning. The
probability that you win the next two matches is
A.
B.
C.
D.
E.
0.06
0.16
0.36
0.40
1.2
4. P(A) = 0.24 and P(B) = 0.52 and A and B are mutually exclusive (disjoint), what is the P(A or B)?
A.
B.
C.
D.
E.
0.1248
0.28
0.6352
0.76
None of the above
5. P(A) = 0.24 and P(B) = 0.52 and A and B are both independent and joint, what is the P(A or B)?
A.
B.
C.
D.
E.
0.1248
0.28
0.6352
0.76
None of the above
PART II: SHOW ALL WORK. USE GOOD NOTATION.
6. Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon
explains the risks to you. Infection occurs in 4% of such operations, the repair fails in 14%, and both
infection and failure occurs together in 1%. (5 points)
A. Draw a Venn diagram to represent this situation.
B. What percent of these operations succeed and are free from infection?
7. Researchers are interested in the relationship between cigarette smoking and lung cancer. Suppose an
adult male is randomly selected from a particular population. Assume that the following
probabilities.
P(smokes and gets cancer) = 0.05
P(smokes and does not get cancer) = 0.20
P(does not smoke and get cancer) = 0.03
P(does not smoke and does not get cancer) = 0.72
P(smokes) = 0.25
a. Find the probability that the individual does not get cancer, given that he does not smoke.
(3 points)
b. Find the probability that the individual gets cancer, given that he is a smoker. (3 points)
c. Are the events that the person does not smoke and gets cancer independent? Show all work. (4
points)
8. Suppose you are given a standard 6-sided die and that the die is “loaded” in such a way that while the
number 1,3,4, and 6 are equally likely to turn up, but the numbers 2 and 5 are four times as likely to
turn up as 1,3,4, and 6. (5 points)
a. What is the probability of rolling a 2?
b. What is the probability of rolling a 1 or a 2?
9. A box contains four red flags numbered 1 to 4 and six white tags numbered 1 to 6. One tag is drawn
at random. ( 2points each = 16 points total)
A. P(Red) =
B. P(Even number) =
C. P(Red and even) =
D. P(Red or even) =
E. P(neither red nor even) =
F. P( Even  red) =
G. P (Red Even) =
H. P(less than 4  odd) =
10. A company that manufactures video cameras produces a basic model and a deluxe model. Over the
past year, 45% of the cameras sold have been the basic model. Of those buying the basic model,
20% purchase an extended warranty, whereas 60% of all purchasers of the deluxe model buy an
extended warranty. If you learn that a randomly selected purchaser bought an extended warranty,
what is the probability that he or she has a basic model? (5 points)
11. Three of the most common pets that people have are cats, dogs, and fish. In fact, many families
have more than one type of pet, and some have all three! Suppose that a family is selected at
random. Define the following events, with the probabilities given. (Note: the fish-and-cats
combination doesn't seem too popular!)
F = a family has at least one pet fish :
D = a family has at least one pet dog:
C = a family has at least one pet cat:
P(F) = 0.20
P(D) = 0.32
P(C) = 0.35
P(F ∩ D) = 0.18; P(F ∩ C) = 0.32; P(D C ) = 0.30
a) Calculate each of the following (show your work): (3 points each = 9 points total)
i) P ( A | D ) =
ii) P(C ∩ D) =
iii) P(A∪D) =
12. One method for increasing sales of boxes of cereal is to suggest to children that they complete a
"set" of small toys. Suppose that the cereal company decides to put the toys in the boxes with
different probabilities. Toy 1 will be put in 30% of the boxes, Toys 2 and 3 will be put in 15% of the
boxes, and Toys 4 and 5 will be put in 20% of the boxes. (10 points)
a) Describe how you would use a random digit table to conduct one run of your simulation, where one
run continues until a complete set of the 5 toys is acquired.
Perform 2 runs, and report the number of boxes needed to buy to get a complete set of 5 toys for each
run. Mark on the random digit table to clearly identify your procedure above.
19223 95734 05756 28713 96409 12531 42544 82853 73676 47150 99400
37754 42648 82425 36290 45467 71709 77558 00095 32863 29485 82226
68417 35013 15529 72765 85089 57067 50211 47487 82739 57890 20807
81676 55300 94383 14893 60940 72024 17868 24943 61790 90656 87964
47140 29385 67067 15803 12589 52167 18568 23243 55770 90846 86664