Ch. 3 - Problems to look at
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) A coin is tossed. Find the probability that the result is heads.
A) 0.5
B) 0.9
C) 0.1
Answer: A
1)
D) 1
2) A single six-sided die is rolled. Find the probability of rolling a number less than 3.
Answer: B
2)
3) A study of 1000 randomly selected flights of a major airline showed that 769 of the flights arrived
on time. What is the probability of a flight arriving on time?
Answer: D
231
1000
1000
769
A)
B)
C)
D)
1000
231
769
1000
3)
4) The distribution of blood types for 100 Americans is listed in the table. If one donor is selected at
random, find the probability of selecting a person with blood type A+.
Answer: A
4)
A) 0.25
Blood Type O+
Number
37
B) 0.333
O6
A+
34
A) 0.34
A6
C) 0.1
B+
10
B2
AB+
4
B) 0.68
D) 0.5
AB1
C) 0.4
D) 0.45
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
5) Identify the sample space of the probability experiment: shooting a free throw in
basketball.
5)
S= {make the shot, miss the shot}
6) Identify the sample space of the probability experiment: recording the number of days it
snowed in Cleveland in the month of January.
6)
S={0,1,2,3,4,5,6,7,.......,31}
7) Identify the sample space of the probability experiment: rolling a single 12-sided die with
sides numbered 1-12
S={1,2,3,4,5,6,7,8,9,10,11,12}
1
7)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your
reasoning.
8) You roll a six-sided die. Event B is rolling an even number.
Answer: A
8)
A) 3; Not a simple event because it is an event that consists of more than a single outcome.
B) 2; Not a simple event because it is an event that consists of more than a single outcome.
C) 1; Simple event because it is an event that consists of a single outcome.
D) 3; Simple event because the die is only rolled once.
9) You randomly select one card from a standard deck. Event B is selecting the ace of hearts.
Answer: A
9)
A) 1; Simple event because it is an event that consists of a single outcome.
B) 4; Simple event because only one card is selected.
C) 13; Not a simple event because it is an event that consists of more than a single outcome.
D) 4; Not a simple event because it is an event that consists of more than a single outcome.
Provide an appropriate response.
10) Which of the following cannot be a probability?
5
A) 0.001
B)
3
11) Rank the probabilities of 10%,
A)
1
, 10%, 0.06
5
Answer: C
C) -68
10)
D) 0
1
, and 0.06 from the least likely to occur to the most likely to occur.
5
B) 0.06, 10%,
1
5
C) 0.06,
1
, 10%
5
12) Classify the events as dependent or independent. Events A and B where
P(A) = 0.7, P(B) = 0.7, and P(A and B) = 0.49
A) dependent
Answer: B
D) 10%,
11)
1
, 0.06
5
Answer: B
12)
Answer: B
13)
B) independent
13) Classify the events as dependent or independent. Events A and B where
P(A) = 0.8, P(B) = 0.1, and P(A and B) = 0.07
A) dependent
B) independent
2
14) A group of students were asked if they carry a credit card. The responses are listed in the table.
Answer: C
Credit Card Not a Credit Card
Class
Carrier
Carrier
Total
Freshman
17
43
60
Sophomore
28
12
40
Total
45
55
100
14)
If a student is selected at random, find the probability that he or she owns a credit card given that
the student is a sophomore. Round your answer to three decimal places.
A) 0.622
B) 0.300
C) 0.700
D) 0.280
15) A group of students were asked if they carry a credit card. The responses are listed in the table.
Answer: D
Credit Card Not a Credit Card
Class
Carrier
Carrier
Total
Freshman
10
50
60
Sophomore
20
20
40
Total
30
70
100
15)
If a student is selected at random, find the probability that he or she is a sophomore and owns a
credit card. Round your answers to three decimal places.
A) 0.667
B) 0.750
C) 0.333
D) 0.200
16) You are dealt two cards successively without replacement from a standard deck of 52 playing
cards. Find the probability that the first card is a two and the second card is a ten. Round your
answer to three decimal places.
Answer: B
A) 0.250
B) 0.006
C) 0.994
16)
D) 0.500
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
17) Find the probability of getting four consecutive aces when four cards are drawn without
replacement from a standard deck of 52 playing cards.
17)
=(4/52)+(3/52)+(2/52)+(1/52)
=0.00000369
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
18) Decide if the events A and B are mutually exclusive or not mutually exclusive. A die is rolled.
Answer: A
A: The result is an odd number.
B: The result is an even number.
A) mutually exclusive
B) not mutually exclusive
3
18)
19) Decide if the events A and B are mutually exclusive or not mutually exclusive, A die is rolled.
Answer: A
A: The result is a 3.
B: The result is an odd number.
A) not mutually exclusive
19)
B) mutually exclusive
20) Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn
from a standard deck of 52 playing cards.
Answer: B
A: The result is a 7.
B: The result is a jack.
A) not mutually exclusive
20)
B) mutually exclusive
21) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a king.
Answer: D
1
4
8
2
A)
B)
C)
D)
13
13
13
13
21)
22) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a black card.
Answer: C
15
29
7
4
A)
B)
C)
D)
26
52
13
13
22)
23) The events A and B are mutually exclusive. If P(A) = 0.6 and P(B) = 0.2, what is P(A or B)?Answer: B
23)
A) 0.12
B) 0.8
C) 0.4
D) 0
24) The table lists the smoking habits of a group of college students.
24)
Sex
Non-smoker Regular Smoker Heavy Smoker Total
Man
135
70
5
210
Woman
187
21
15
223
Total
322
91
20
433
If a student is chosen at random, find the probability of getting someone who is a man or a
non-smoker. Round your answer to three decimal places.
Answer: D
A) 0.950
B) 0.790
C) 0.942
D) 0.917
25) The events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A and B)?
Answer: C
A) 0.12
B) 0.5
C) 0
4
D) 0.7
25)
Solve the problem.
26) There are 3 balls in a hat; one with the number 2 on it, one with the number 4 on it, and one with
the number 9 on it. You pick a ball from the hat at random and then you flip a coin. Using a tree
diagram , obtain the sample space for the experiment. List the elements that make up the sample
space.
Answer: D
A) 2 4 9 H, 2 4 9 T
B) 2 H, 4 H, 9 H
C) 2 H T, 4 H T, 9 H T
D) 2 H, 2 T, 4 H, 4 T, 9 H, 9 T
27) Which of the following events are mutually exclusive?
Answer: C
26)
27)
A) being a college student and being a high school graduate
B) being a steelworker and being a stamp collector
C) being a mother and being an uncle
D) living in Baltimore and working in Washington, D.C.
E) none of these
28) Two events A and B are mutually exclusive if
A) A
Answer: D
28)
B = U.
B) A B =
.
C) A B = U.
D) A
B=
.
E) none of these
29) Two fair die are rolled. What is the probability that the numbers that appear are both 3? Answer: B
1
A)
3
B)
1
36
C)
1
2
D)
1
6
29)
E) none of these
30) Let E and F are mutually exclusive and Pr(E) = 0.2 and Pr(F) = 0.6. Find Pr(E
A) 0.12
B) 0
C) 1
D) 0.8
E) none of these
5
F).
Answer: D
30)
A basket contains five red balls, four white balls and three blue balls. Two balls are drawn, one after the other, with the
first ball replaced before the second is drawn.
31) Find the probability of drawing two white balls.
1
A)
9
B)
4
1
=
12 3
C)
2
1
=
12 6
D)
2
9
Answer: A
31)
E) none of these
Solve the problem.
32) Two coins are tossed 20 times and the number of tails is observed.
Outcome
Frequency
Answer: B
32)
2 tails 1 tail 0 tails
3
7
10
Compute the empirical probability that exactly one tail occurred.
1
7
17
A)
B)
C)
4
20
20
D)
1
2
Estimate the indicated probability.
33) The table shows the number of college students who prefer a given pizza topping. Answer: D
toppings freshman sophomore junior
senior
cheese
10
15
26
21
meat
24
21
15
10
veggie
15
10
24
21
33)
Determine the empirical probability that a junior prefers meat toppings.
A) 0.071
B) 0.214
C) 0.320
D) 0.231
Find the probability.
34) A bag contains 2 red marbles, 4 blue marbles, and 8 green marbles. What is the probability of
choosing a blue marble?
Answer: B
2
2
1
4
A)
B)
C)
D)
3
7
7
7
6
34)
35) Determine the probability that the spinner lands on white.
A) 1
B)
1
4
C)
1
2
Answer: B
D)
35)
1
3
36) A fair die is rolled. What is the probability of rolling an odd number or a number less than 3?
Answer: A
2
1
5
A)
B)
C)
D) 1
3
2
6
36)
37) A bag contains 8 red marbles, 2 blue marbles, and 1 green marble. What is the probability of
choosing a marble that is not blue?
Answer: A
9
11
2
A)
B) 9
C)
D)
11
9
11
37)
Solve the problem.
38) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.
Answer: A
1
1
A) 0
B)
C) 1
D)
6
2
38)
Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the
probability.
39) The second marble is white given the first marble is blue.
3
3
3
A)
B)
C)
56
64
7
7
Answer: C
3
D)
8
39)