Unit 4
1. A six-sided die has faces numbered 1, 2, 3, 4, 5 and 6. Suppose the die is “loaded”, so
that any particular even-numbered face is twice as likely to land face up as any particular
odd-numbered face. If we roll this die once, what is the probability that the number
showing is greater than 3?
(A)
1
2
(B)
2
3
(C)
5
9
(D)
7
12
(E)
9
16
2. A hat contains one gold coin, one silver coin and one copper coin. You will randomly
select coins, without replacement, until the gold coin is selected. The outcome of interest
is the sequence of colours that are selected during this process. How many outcomes are
contained in the appropriate sample space for this experiment?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
3. A hat contains 10 gold coins, 10 silver coins and 10 copper coins. We randomly select
four coins from the hat. Let A be the event that the first selected coin is the only gold
coin in our four selections. Which of the following events is mutually exclusive of the
event A?
(A) second coin selected is silver
(B) no copper coins are selected
(C) third selected coin is the only silver coin
(D) same number of gold and copper coins are selected
(E) same number of silver and copper coins are selected
4. A tourist is flying home from Cairo, Egypt to Winnipeg. She must change planes in
Berlin, London and Toronto. Her suitcase is placed on her plane flying from Cairo to
Berlin. Suppose we have the following facts:
• 5% of all suitcases are lost at the airport in Berlin.
• 8% of all suitcases are lost at the airport in London.
• 7% of all suitcases are lost at the airport in Toronto.
What is the probability that the tourist’s suitcase arrives safely in Winnipeg?
(A) 0.80
(B) 0.81
(C) 0.82
(D) 0.83
(E) 0.84
The next two questions (5 and 6) refer to the following:
The following six games are being played in the National Hockey League one night. The
values in parentheses are the probabilities of each team winning their respective game:
Game 1:
Game 2:
Game 3:
Game 4:
Game 5:
Game 6:
Tampa Bay Lightning (0.57) vs. New York Rangers (0.43)
Boston Bruins (0.58)
vs. New York Islanders (0.42)
Winnipeg Jets (0.63)
vs. Vancouver Canucks (0.37)
Chicago Blackhawks (0.72)
vs. Arizona Coyotes (0.28)
Colorado Avalanche (0.52)
vs. Detroit Red Wings (0.48)
San Jose Sharks (0.56)
vs. Anaheim Ducks (0.44)
5. The outcome of interest is the set of winners for each of the six games. How many
outcomes are contained in the appropriate sample space?
(A) 12
(B) 32
(C) 36
(D) 64
(E) 128
6. What is the probability that Winnipeg wins or that both New York teams win?
(A) 0.6968
(B) 0.7245
(C) 0.7514
(D) 0.7833
(E) 0.8106
7. Consider two independent events A and B. Suppose it is known that P (A) = 0.27 and
P (A or B) = 0.5474. What is P (B)?
(A) 0.38
(B) 0.46
(C) 0.29
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(D) 0.33
(E) 0.41
8. Events A and B are independent. It is known that P (B) = 0.43 and P (A ∪ B) = 0.7777.
What is the probability of the event A?
(A) 0.61
(B) 0.62
(C) 0.63
(D) 0.64
(E) 0.65
9. An event A has probability 0.7. An event B has probability 0.6. If A and B are
independent, which of the following are true?
(I)
(II)
(III)
P (A ∩ B) = 0.42
P (A ∪ B) = 0.88
P (B|A) = 0.6
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
10. A box contains one red ball and one black ball. One ball is randomly selected from the
box. It is then replaced in the box along with an extra ball of the same colour. This
process is repeated several times. What is the probability that a red ball is selected on
the first three draws?
(A) 1/3
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/9
11. A discrete random variable X has the probability distribution shown below:
1
2
3
4
5
6
7
8
9
10
x
P (X = x) 0.04 0.08 0.12 0.05 0.10 0.07 0.15 0.09 0.16 0.14
What is P (X is a multiple of 3 | X is not a multiple of 2)?
(A) 0.47
(B) 0.48
(C) 0.49
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(D) 0.50
(E) 0.51
12. It is known that 41% of students at a large university are taking a Statistics course, 29%
are taking a Calculus course, and 17% are taking both Statistics and Calculus. What is
the probability that a randomly selected student is taking Statistics if he is not taking
Calculus?
(A) 0.305
(B) 0.316
(C) 0.327
(D) 0.338
(E) 0.349
13. Claim amounts for a large insurance company follow a normal distribution with mean
$35,000 and standard deviation $10,000. The company defines a large claim to be one
whose value exceeds $50,000. If a randomly selected claim is a large claim, what is the
probability it is valued at over $60,000?
(A) 0.0928
(B) 0.1814
(C) 0.1255
(D) 0.0637
(E) 0.1546
14. In Vancouver, 42% of the days are rainy. Mary takes the bus 65% of the days. On 37%
of days, she takes the bus and the weather is rainy. What is the probability that she
takes the bus if the weather is not rainy?
(A) 0.3595
(B) 0.3919
(C) 0.4363
(D) 0.4828
(E) 0.5424
15. For a certain course, it is known that 12% of students fail the midterm, 9% fail the final,
and 5% fail both the midterm and the final. What is the probability that a student will
fail the final exam if he passed the midterm?
(A) 0.0122
(B) 0.0233
(C) 0.0344
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(D) 0.0455
(E) 0.0566
The next two questions (16 and 17) refer to the following:
Three piggy banks each contain 20 coins:
• Piggy Bank # 1 contains 12 gold coins, 5 silver coins and 3 copper coins.
• Piggy Bank # 2 contains 8 gold coins, 10 silver coins and 2 copper coins.
• Piggy Bank # 3 contains 6 gold coins, 9 silver coins and 5 copper coins.
16. If we randomly select one coin from each piggy bank, what is the probability we get
exactly one gold coin?
(A) 0.333
(B) 0.367
(C) 0.400
(D) 0.436
(E) 0.475
17. If we randomly select two coins from Piggy Bank # 3 without replacement, what is the
probability the two coins we select are the same colour?
(A) 0.321
(B) 0.333
(C) 0.346
(D) 0.355
(E) 0.367
18. A professor gives her class a short multiple choice quiz one day. There are three questions
on the quiz. The first question has three possible answers (A, B, C), the second question
has four possible answers (A, B, C, D) and the third question has five possible answers (A,
B, C, D, E). An unprepared student randomly guesses the answer to each of the three
questions. What is the probability that the student gets exactly one of the answers
correct?
(A) 0.3167
(B) 0.4333
(C) 0.5667
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(D) 0.6725
(E) 0.7833
The next two questions (19 and 20) refer to the following:
A bowl contains five yellow candies, three red candies and two orange candies.
19. If we randomly select two candies without replacement, what is the probability that
we get at least one orange candy?
(A) 0.3556
(B) 0.3600
(C) 0.3667
(D) 0.3778
(E) 0.3833
20. We randomly select two candies with replacement. Given that both of the selected
candies are the same colour, what is the probability that they are both yellow?
(A) 0.2500
(B) 0.3333
(C) 0.4468
(D) 0.5275
(E) 0.6579
21. In a game of poker, you are dealt five cards from a deck of 52 cards. What is the
probability that you get a flush (five cards of the same suit)?
(A) 0.0005
(B) 0.0010
(C) 0.0020
(D) 0.0030
(E) 0.0040
22. We have a small deck of ten cards. Seven of the cards are red and three of the cards are
blue. We will repeatedly select cards from the deck at random, without replacement,
until we select a blue card for the first time. What is the probability the first blue card
is chosen on the fourth selection?
(A) 0.103
(B) 0.116
(C) 0.125
(D) 0.137
(E) 0.142
23. A dish contains three cherry candies, four lemon candies and five grape candies. If we
randomly select two candies from the dish without replacement, what is the probability
that we get one cherry candy and one grape candy?
(A) 0.1042
(B) 0.1136
(C) 0.1628
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(D) 0.2085
(E) 0.2273
24. In a particular election, 40% of voters voted for the NDP, 35% voted for the Liberals
and 25% voted for the Conservatives. If we take a random sample of two voters, what
is the probability that they voted for different parties?
(A) 0.345
(B) 0.465
(C) 0.575
(D) 0.655
(E) 0.715
25. A taxi can accommodate anywhere from one to four passengers at a time. The number
of passengers X per ride for one taxi has the probability distribution shown below:
1
2
3
4
x
P (X = x) 0.3 0.4 0.2 0.1
What is the probability that there are at least 7 passengers in the taxi’s next two rides?
(A) 0.04
(B) 0.01
(C) 0.05
(D) 0.03
(E) 0.02
26. You have three unfair coins. When flipped, the coins have the following probabilities of
landing on Heads:
P (Heads)
0.47
0.56
0.68
Coin 1
Coin 2
Coin 3
If you flip each coin, what is the probability that exactly two of them land on Heads?
(A) 0.3750
(B) 0.3844
(C) 0.4267
(D) 0.4656
(E) 0.5133
27. We have two bowls, each containing several gumballs:
• Bowl 1 contains 5 red gumballs and 3 blue gumballs.
• Bowl 2 contains 3 red gumballs and 2 blue gumballs.
John will randomly select two gumballs from Bowl 1 without replacement. Jane will
randomly select two gumballs from Bowl 2 with replacement. What is the probability
that all four gumballs selected by the two friends are the same colour?
(A) 0.1178
(B) 0.1312
(C) 0.1457
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(D) 0.1564
(E) 0.1631
Answers
1. C
2. B
3. E
4. B
5. D
16. D
17. A
18. B
19. D
20. E
6. A
7. A
8. A
9. E
10. B
21. C
22. C
23. E
24. D
25. C
11. C
12. D
13. A
14. D
15. D
26. C
27. C
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