Name: __________________________ Date: _____________
1. I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair; that is, the probability of heads is
1 and the probability of tails is 1 . This means
2
2
A) that every occurrence of a head must be balanced by a tail in one of the next two or three tosses.
B) that if I flip the coin many, many times, the proportion of heads will be approximately 1 2 , and this proportion will
C)
D)
E)
tend to get closer and closer to 1 2 as the number of tosses increases.
that regardless of the number of flips, half will be heads and half tails.
generally, the flips will alternate between heads and tails.
all of the above.
2. If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a
large number of repetitions, we say the phenomenon is
A) random.
B) predictable.
C) deterministic.
D) probabilistic.
E) none of the above.
3. I toss a thumbtack 60 times and it lands point up on 35 of the tosses. The approximate probability of landing point up is
A) 35.
B) 0.35.
C) 0.58.
D) 0.65.
E) 58.
4. Suppose we have a loaded die that gives the outcomes 1–6 according to the following probability distribution:
X
P(X)
1
0.1
2
0.2
3
0.3
4
0.2
5
0.1
6
0.1
Note that for this die all outcomes are not equally likely, as they would be if the die were fair. If this die is rolled 6000
times, the number of times we get a 2 or a 3 should be about
A) 1000.
B) 2000.
C) 3000.
D) 4000.
E) The answer cannot be determined since the probabilities are only approximate.
5. Suppose we roll a red die and a green die. Let A be the event that the number of spots showing on the red die is 3 or less
and B be the event that the number of spots showing on the green die is more than 3. The events A and B are
A) disjoint.
B) complements.
C) independent.
D) reciprocals.
E) dependent.
6. In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5, you win $1; if the number of
spots showing is 6, you win $4; and if the number of spots showing is 1, 2, or 3, you win nothing. If it costs you $1 to
play the game, the probability that you win more than the cost of playing is
A) 0.
B) 1/6.
C) 1/3.
D) 2/3.
E) 5/6.
A public opinion survey explored the relationship between age and support for increasing the minimum wage.
The results are summarized in the two-way table.
7.
A)
B)
C)
D)
E)
What is the probability that someone over 60 is against it?
20%
21%
35%
7.5%
There is no way to tell.
8. What is the probability that someone is over 60 or against it?
A) 65%
B) 75%
C) 50%
D) 72.5%
E) 80%
Use the following to answer questions 9-12:
If you draw an M&M candy at random from a bag of M&M's, the candy you draw will have one of six colors. The probability of
drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probability
that a randomly chosen M&M has each color.
Color
Probability
Brown
.3
Red
.3
Yellow
?
Green
.1
Orange
.1
9. The probability of drawing a yellow candy is
A) 0.1.
B) 0.2.
C) 0.3.
D) 3.
E) impossible to determine from the information given.
10. The probability of not drawing a red candy is
A) 0.1.
B) 0.3.
C) 0.6.
D) 0.7.
E) 0.9.
11. The probability of drawing neither a brown nor a green candy is
A) 0.1.
B) 0.3.
C) 0.4.
D) 0.6.
E) 0.7.
Tan
.1
12. If two M&M's are selected and the colors are independent, then the probability that both are the same
color is
A) 0.01.
B) 0.03.
C) 0.09.
D) 0.22.
E) 0.25.
13. Event A occurs with probability 0.3. If event A and B are disjoint, then
A) P(B) ≤ 0.3.
B) P(B) ≥ 0.3.
C) P(B) ≤ 0.7.
D) P(B) ≥ 0.7.
E) P(B) = 0.21.
14. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually
exclusive), then
A) P(A and B) = 0.16.
B) P(A and B) = 0.84.
C) P(A and B) = 1.
D) P(A or B) = 0.16.
E) P(A or B) = 1.
Use the following to answer questions 16-17:
A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card
before selecting the second card.
16. Referring to the information above, consider the events
A = the first card selected is red
B = the second card selected is red
The events A and B are
A) dependent.
B) disjoint.
C) complements.
D) independent.
E) none of the above.
17. Referring to the information above, consider the events
A = the first card selected is red
B = the second card selected is black
The events A and B are
A) independent.
B) disjoint.
C) complements.
D) reciprocals.
E) none of the above.
18. Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3. P(A or B) =
A)
B)
C)
D)
E)
0.09.
0.51.
0.52.
0.57.
0.60.
19. Suppose that A and B are two independent events with P(A) = 0.2 and P(B) = 0.4.
P(A ∩ BC) is
A) 0.08.
B) 0.12.
C) 0.52.
D) 0.60.
E) 0.92.
20. In a certain town 60% of the households own a cellular phone, 40% own a pager, and 20% own both a cellular phone and
a pager. The proportion of households that own a cellular phone but not a pager is
A) 20%.
B) 30%.
C) 40%.
D) 50%.
E) 80%.
Use the following to answer questions 25-26:
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is
0.1.
25. Referring to the information above, the conditional probability of A given B
A) is 0.3.
B) is 0.2.
C) is 1/6.
D) is 0.1.
E) cannot be determined from the information given.
26. Referring to the information above, we may conclude
A) that events A and B are independent.
B) that events A and B are complements.
C) that either A or B always occurs.
D) that events A and B are disjoint.
E) none of the above.
27. What is the probability of A or B but not both?
A) 0.5
B) 0.8
C) .9
D) 1
28. Event A occurs with probability 0.8. The conditional probability that event B occurs given that A occurs is
0.5. The probability that both A and B occur
A) is 0.3.
B) is 0.4.
C) is 0.5.
D) is 0.8.
E) cannot be determined from the information given.
29. Event A occurs with probability 0.3 and event B occurs with probability 0.4. If A and B are independent,
we may conclude that
A) P(A and B) = 0.12.
B) P(A|B) = 0.3.
C) P(B|A) = 0.4.
D) P(A or B) = 0.58.
E) all of the above.
30. The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.001.
The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.99
for a person with the disease and 0.02 for a person without the disease. The proportion of adults for which the test would be
positive is
A) 0.00002.
B) 0.00099.
C) 0.01998.
D) 0.02097.
E) 0.02100.
31. In question 38, if a randomly selected person is tested and the result is positive, the probability the
individual has the disease is
A) 0.001.
B) 0.019.
C) 0.020.
D) 0.021.
E) 0.047.
Answer Key
1. B
2. A
3. C
4. C
5. C
6. B
7. A
8. A
9. A
10. D
11. D
12. D
13. C
14. E
16.
17.
18.
19.
20.
25.
26.
27.
28.
29.
30.
31.
A
E
B
B
C
C
C
C
B
E
D
E