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A.P. Statistics Extra Probability Practice
Use the following table to answer questions 1 through 8.
Results From Experiments With Polygraph Instruments
Did the Subject Actually lie?
No
Yes
Positive Test Result
15
42
Negative Test Result
32
9
1. What is the probability that when someone takes the test it reads positive?
2. What is the probability that a person lies and the test is positive?
3. What is the probability that a person lies and the test is negative?
4. What is the probability that if a person tells the truth, they test positive?
5. What is the probability that if a person tells the truth, they test negative?
6. What is the probability that if a person lies, the detector does not catch it?
7. What is the probability that if a person lies, the detector catches it?
8. Are the events lying and having a negative test result independent?
9. Women have a 25% rate of red/green colorblindness. If two women are randomly selected, what is the probability
that they are both red/green colorblind?
10. Using the information from #9, what is the probability that if you have a classroom of 20 women at least one is
red/green colorblind?
11. With one method of a procedure called acceptance sampling, a sample of items is randomly selected without
replacement and the entire batch is accepted if there are no mistakes. The Telektronics Company manufactured a batch
of 400 backup power supply units for computers, and 8 of them are defective. What is the probability that the entire
batch is accepted when they randomly select three of the units?
12. In a case in Riverhead, New York, nine different crime victims listened to a voice recording of five different men to
identify the criminal. All nine victims identified the same person. If the answers were just random guesses with no
validity, what is the probability that the victims would all identify the same person? Is this reasonable doubt (that this
man could not be the criminal?
13. The FICO score is commonly used as a credit rating. There is a 1% delinquency rate among consumers who have a
FICO score above 800. If four consumers with FICO scores above 800 are randomly selected, what is the probability that
at least one of them becomes delinquent?
14. Suppose there is an outbreak of a rare disease in the United States. It is estimated that 1 in every 1000 people will
contract the disease. A diagnostic test is available that is 97% accurate for people who have the disease, and 95%
accurate for people who do not have the disease.
a. What is the probability that a randomly selected person tests positive?
b. Given that the person has tested positive for the disease, what is the probability that the person actually has the
disease?
15. At a certain school, 22% of the students are in concert band and 35% of the students are in concert choir, and
9% of the students are in chamber choir. 3% of the students are in chamber choir and concert band, 6% of the
students are in concert choir and concert band, 6% of the students are in chamber choir and concert choir, and 2%
are in all three. If a student is chosen at random, what is…
a.
P(concert choir only) = ?
b. P(concert band only) = ?
c. P( chamber choir only) = ?
d. P(choir and not band) = ?
e. P(concert band or concert choir) = ?
f. P(band or choir) = ?
g. P(neither band nor choir) = ?
h. P(chamber and concert choir and not band) = ?
16. A company retains a psychologist to assess whether job applicants are suited for assembly-line work. The
psychologist classifies applicants as A (well suited), B (marginal), or C (not suited). The company in concerned about the
event D: an employee leaves the company within a year of being hired. Data on all people hired in the past 5 years give
these probabilities:
P(A) = 0.4
a. P(D) = ?
P(B) = 0.3
P(C) = 0.3
P(A and D) = 0.1
P(B and D) = 0.1
P(C and D) = 0.2