AP STAT
CHAPTER 6 REVIEW
Probability
Wheeler High School
SPRING 2008
Section 1: Multiple choice
1.
Events A and B defined by the given Venn diagram are
(A)
(B)
(C)
(D)
(E)
2.
A
S
If performance on AP Stat tests are independent and the probability of passing an AP Stat
test is 0.2, then the probability of passing three AP Stat tests is
(A)
(B)
(C)
(D)
(E)
3.
independent and disjoint
dependent and disjoint
independent and not disjoint
dependent and not disjoint
cannot be determined
0
0.008
0.04
0.2
0.6
If P( X)  0.23 , P( X  Y)  0.12 , and P( X  Y)  0.34 , then find P(YC) .
(A)
(B)
(C)
(D)
(E)
0.11
0.23
0.48
0.52
0.77
B
AP STAT
CHAPTER 6 REVIEW
Probability
4.
If two fair dice are rolled, what is the probability of getting a sum greater than 4?
(A)
(B)
(C)
(D)
(E)
5.
0.167
0.333
0.500
0.667
0.833
How many possible 5-character code words are possible if the first two characters are letters
and the last three characters are numbers (and no character may be repeated)?
(A)
(B)
(C)
(D)
(E)
6.
SPRING 2008
p. 2
78
82
468,000
676,000
the number is too large for my calculator
In a certain game, a fair die is rolled and a player gains 20 points if the die shows a “6.” If
the die does not show a “6,” the player loses 3 points. If the die were to be rolled 100 times,
what would be the expected total gain or loss for the player?
(A)
(B)
(C)
(D)
(E)
a gain of about 1,700 points
a gain of about 583 points
a gain of about 83 points
a loss of about 250 points
a loss of about 300 points
AP STAT
CHAPTER 6 REVIEW
Probability
SPRING 2008
p. 3
Section 2: Free-response questions
7. In April 2003, Science magazine reported on a new computer-based test for ovarian
cancer, “clinical proteomics,” that examines a blood sample for the presence of certain
patterns of proteins. Ovarian cancer, though dangerous, is very rare, afflicting only 1 of
every 5000 women. The test is highly sensitive, able to correctly detect the presence of
ovarian cancer in 99.97% of women who have the disease. However, it is unlikely to be
used as a screening test in the general population because the test gave false positives
5% of the time. Why are false positives such a big problem? Draw a tree diagram and
determine the probability that a woman who tests positive using this method actually
has ovarian cancer.
8.
If P( A)  0.2 and P( B)  0.3 , find P( A  B) if
(a) A and B are independent
(b) A and B are disjoint
AP STAT
CHAPTER 6 REVIEW
SPRING 2008
p. 4
Probability
9.
In a recent survey of 100 10-year olds, the following information was obtained:
53 liked McDonalds
24 liked Burger King
42 liked Wendy’s
6 liked all three
12 liked both McDonalds and Burger King
23 liked both McDonalds and Wendy’s
4 liked only Burger King
(a) Draw a Venn diagram illustrating this information.
(b) How many 10-year olds don’t like any of these three?
(c) What percentage of these 10-year olds like Burger King and Wendy’s?
(d) If one of these 10-year olds likes Wendy’s, what is the probability that he likes Burger
King?
10. A company that manufactures video cameras produces a basic model and a deluxe model.
Over the past year, 40% of the cameras sold have been the basic model. Of those buying the
basic model, 30% purchase an extended warranty; whereas, 50% of all purchasers of the
deluxe model buy an extended warranty. Draw a tree diagram of this situation showing the
probabilities of all possible events.
If you learn that a randomly selected purchaser bought an extended warranty, what is the
probability that he or she has a basic model?