Review Sheet: Chapter 3 - Probability
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1. Given the following probabilities, which event is most likely to occur?
A. P(A) = 0.28
B.
P(B) =
C. P(C) = 0.27
D.
P(D) =
____
2. Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls
out a coin at random. Determine the odds against the coin being a quarter.
A.
B.
C.
D.
____
3. Julie draws a card at random from a standard deck of 52 playing cards. Determine the odds in favour of the
card being a heart.
A.
B.
C.
D.
____
0.250
0.500
0.625
0.750
7. The weather forecaster says that there is a 30% probability of fog tomorrow. Determine the odds against
fog.
A.
B.
C.
D.
____
0.250
0.333
0.750
0.848
6. Julie draws a card at random from a standard deck of 52 playing cards. Determine the probability of the
card being a diamond.
A.
B.
C.
D.
____
3:5
3:8
5:8
5:3
5. Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls
out a coin at random. Determine the probability of the coin being a quarter.
A.
B.
C.
D.
____
3:1
1:3
1:1
3 : 13
4. Tia notices that yogurt is on sale at a local grocery store. The last eight times that yogurt was on sale, it was
available only three times. Determine the odds against yogurt being available this time.
A.
B.
C.
D.
____
1:4
1:3
3:4
3:1
3:7
3 : 10
7:3
7 : 10
8. A sports forecaster says that there is a 40% probability of a team winning their next game. Determine the
odds against that team winning their next game.
A.
B.
C.
D.
2:3
2:5
3:5
3:2
____
9. From a committee of 18 people, 2 of these people are randomly chosen to be president and secretary.
Determine the number of ways in which these 2 people can be chosen for president and secretary.
A.
B.
C.
D.
____
18P2
18P12
17.23%
22.61%
27.35%
34.06%
17 456
25 872
29 778
35 910
28.57%
33.45%
39.06%
46.91%
12.5%
37.5%
62.5%
87.5%
15. Two dice are rolled. Let A represent rolling a sum greater than 7. Let B represent rolling a sum that is a
multiple of 3. Determine n(A  B).
A.
B.
C.
D.
____
18P4
14. Yvonne tosses three coins. Determine the probability that at least one coin will land as heads.
A.
B.
C.
D.
____
18P16
13. Four boys and three girls will be riding in a van. Only two people will be selected to sit at the front of the
van. Determine the probability that only boys will be sitting at the front.
A.
B.
C.
D.
____
18P16
12. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip.
Determine the number of ways in which there can be more girls than boys on the trip.
A.
B.
C.
D.
____
18P2
11. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip.
Determine the probability that there will be equal numbers of boys and girls on the trip.
A.
B.
C.
D.
____
2P1
10. From a committee of 18 people, 2 of these people are randomly chosen to be president and secretary.
Determine the total number of possible committees.
A.
B.
C.
D.
____
2P2
5
8
12
15
16. Select the events that are mutually exclusive.
A. Drawing a 7 or drawing a heart from a standard deck of 52 playing cards.
B. Rolling a sum of 4 or rolling an even number with a pair of four-sided dice, numbered 1 to
4.
C. Drawing a black card or drawing a Queen from a standard deck of 52 playing cards.
D. Rolling a sum of 8 or a sum of 11 with a pair of six-sided dice, numbered 1 to 6.
____
17. Roena is about to draw a card at random from a standard deck of 52 playing cards. Determine the
probability that she will draw a heart or a King.
A.
B.
C.
D.
____
18. Hilary draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card
from the deck without replacing the first card. Determine the probability that both cards are hearts.
A.
B.
C.
D.
____
19. Min draws a card from a well-shuffled standard deck of 52 playing cards. Then she puts the card back in the
deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are
face cards.
A.
B.
C.
D.
____
20. Select the events that are dependent.
A. Rolling a 2 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6.
B. Drawing an odd card from a standard deck of 52 playing cards, putting it back, and then
drawing another odd card.
C. Drawing a spade from a standard deck of 52 playing cards and then drawing another
spade, without replacing the first card.
D. Rolling an even number and rolling an odd number with a pair of six-sided dice, numbered
1 to 6.
____
21. Select the events that are independent.
A. Drawing a 10 from a standard deck of 52 playing cards and then drawing another card,
without replacing the first card.
B. Rolling a 4 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6.
C. Choosing a number between 1 and 20 with the number being a multiple of 3 and also a
multiple of 9.
D. Drawing a diamond from a standard deck of 52 playing cards and then drawing another
diamond, without replacing the first card.
____
22. There are 60 males and 90 females in a graduating class. Of these students, 30 males and 50 females plan to
attend a certain university next year. Determine the probability that a randomly selected student plans to
attend the university.
A.
B.
C.
D.
0.41
0.47
0.53
0.59
____
23. Paul has four loonies, three toonies, and five quarters in his pocket. He needs two quarters for a parking
meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both
coins are quarters.
A.
B.
C.
D.
____
24. A four-sided red die and a six-sided green die are rolled. Determine the probability of rolling a 2 on the red
die and a 5 on the green die.
A.
B.
C.
D.
____
4.17%
4.89%
6.50%
8.04%
25. Two cards are drawn, without being replaced, from a standard deck of 52 playing cards. Determine the
probability of drawing a face card then drawing an even-numbered card.
A.
B.
C.
D.
____
15.15%
19.64%
26.47%
32.13%
1.96%
9.05%
14.32%
23.08%
26. Select the independent events.
A.
B.
C.
D.
P(A) = 0.67, P(B) = 0.12, and P(A  B) = 0.086
P(A) = 0.83, P(B) = 0.4, and P(A  B) = 0.378
P(A) = 0.4, P(B) = 0.91, and P(A  B) = 0.364
P(A) = 0.2, P(B) = 0.32, and P(A  B) = 0.046
Short Answer
1. A credit card company randomly generates temporary five-digit pass codes for cardholders. Meghan is
expecting her credit card to arrive in the mail. Determine, to the nearest hundredth of a percent, the
probability that her pass code will consist of five different even digits.
2. From a committee of 12 people, 3 of these people are randomly chosen to be president, vice-president, and
secretary. Determine, to the nearest hundredth of a percent, the probability that Pavel, Rashida, and Jerry
will be chosen.
3. Access to a particular online game is password protected. Every player must create a password that consists
of three capital letters followed by two digits. Repetitions are NOT allowed in a password. Determine, to
the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters
J, K, and L.
4. Ashley has letter tiles that spell NAPKIN. She has selected three of these tiles at random. Determine the
probability that the tiles she selected are two consonants and one vowel.
Problem
1. Three people are running for president of the student council. The polls show Denis has a 55% chance of
winning, Cyndi has a 25% chance of winning, and Chris has a 20% chance of winning.
a) What are the odds in favour of each person winning? Show your work.
b) Suppose that Chris withdraws and offers his support to Cyndi. Further suppose that his supporters also
switch to Cyndi. What are the odds in favour of Cyndi winning now?
2. Atian, Sam, Phuong, Mike, and Tariq are competing with ten other boys to be on their school’s
cross-country team. All the boys have an equal chance of winning the trial race. Determine the probability
that Atian, Sam, Phuong, Mike, and Tariq will place first, second, third, fourth, and fifth, in any order.
Show your work.
3. A student council consists of 12 girls and 8 boys. To form a subcommittee, 4 students are randomly selected
from the council. Determine the odds in favour of 3 girls and 1 boy being on the subcommittee. Show your
work.
4. A car manufacturer keeps a database of all the cars that are available for sale at all the dealerships in
Western Canada. For model A, the database reports that 36% have heated leather seats, 41% have a sunroof,
and 52% have neither. Determine the probability of a model A car at a dealership having both heated leather
seats and a sunroof. Show your work.
5. A survey reported that 29% of households have one or more dogs, 35% have one or more cats, and 42%
have neither dogs nor cats. Suppose that a household is selected at random. Determine the probability that
there are cats but no dogs in the household. Show your work.
6. Aisha plays the balloon pop game at a carnival. There are 50 balloons, with the name of a prize inside each
balloon. The prizes are 10 stuffed bears, 6 toy trucks, 21 decks of cards, 9 yo-yos, and 4 giant stuffed dogs.
Aisha pops a balloon with a dart. Determine the odds in favour of her winning either a stuffed dog or a
stuffed bear. Show your work.
7. On Tuesday, the weather forecaster says that there is a 40% chance of snow on Wednesday and a 50%
chance of snow on Thursday. The forecaster also says that there is a 10% chance of snow on both
Wednesday and Thursday. Determine the probability that there will be snow on Wednesday or on Thursday.
Show your work.
8. A jar contains 8 green marbles and some green marbles. The odds against selecting a randomly chosen
red marble are 1:5. Show all workings to determine A) how many green marbles are in the jar B)total
number of marbles in the jar.
9. A 6 digit number is generated from the following digits 3, 2, 7, 9, 6, 5 with no repetition. Find the
probability of the number that is formed that is will be:
A)
B)
C)
An odd number
An even number
The odds against an even number being formed
10. There are 13 teachers and 5 administrators at a conference.
A)
B)
C)
Find the number of ways you can award 3 prizes to teachers only.
Find the number ways to give out the four prizes to all people at the conference?
Find the probability that all of the 3 prizes went to teachers? To Administrators?
11. A jar contains 5 red, 8 blue and 10 purple candies. If the total number of candies is 30, find the probability
that a handful of 4 contains one of each type?
12. Mark, Nancy, Olivia, Paul, Quinlan, Victor, and Roxy are standing in a line.
A)
B)
C)
Determine the total possible arrangements.
Determine how many ways Quinlan and Roxy could be standing together. Use this to determine
the probability Mark and Nancy will be standing together? What are odds this will NOT be
standing together?
What is the probability that Paul and Quinlan are NOT standing together?
13. In a class survey, 61% play sports, 37% play a musical instrument, 19% play neither. Draw a Venn diagram
to illustrate whether the events are mutually exclusive or non-mutually exclusive. Use it to determine
A) the probability someone play a musical instrument or plays sports
B) the probability someone does not play a musical instrument
C) the probability someone plays a sport only
14. A person is being selected to draw a marble from a bag. The odds of selecting a male from the group are
7:10 while the odds of selecting a green marble are 1: 4. What is the PROABILITY of a non-green marble
being selecting by a female in the group? (AND is implied YES or NO?)
Review Sheet
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
B
B
D
C
A
C
D
A
C
D
B
A
D
A
D
A
B
B
C
B
A
A
A
B
C
SHORT ANSWER
1. ANS:
0.12%
2. ANS:
0.45%
3. ANS:
0.038%
4. ANS:
60%
PROBLEM
1. ANS:
a) The odds in favour of Denis winning are 55 : (100 – 55). This is equal to 55: 45 or 11 : 9. The
odds in favour of Cyndi winning are 25 : (100 – 25). This is equal to 25 : 75 or 1 : 3. The odds in
favour of Chris winning are 20 : (100 – 20). This is equal to 20 : 80 or 1 : 4.
b) If Chris’ 20% support goes to Cyndi, then her support will now be 45%, and the odds in favour
of Cyndi winning will be the same as the odds against Denis winning. So, the odds in favour of
Cyndi winning are 45 : 55 or 9 : 11.
2. ANS:
Atian, Sam, Phuong, Mike, and Tariq can place first, second, third, fourth, or fifth, in any order.
There are 5! or 120 ways in which five runners can place in five positions.
There are 15P5 ways that 15 runners can place first, second, third, fourth, or fifth.
There are 360 360 possible outcomes.
P(A, S, P, M, and T place 1, 2, 3, 4, or 5) =
P(A, S, P, M, and T place 1, 2, 3, 4, or 5) =
or
The probability that Atian, Sam, Phuong, Mike, and Tariq will place in the top five positions is
or about 0.03%.
3. ANS:
Let T represent three girls and one boy being chosen to form a subcommittee, and let S represent
all possible subcommittees.
In this example, order is not important. The number of ways to arrange three girls and one boy
from 12 girls and 8 boys is 12C3  8C1.
The number of ways to arrange 20 people in a four-person committee is 20C4.
The probability can now be determined:
The odds in favour that the committee will contain 3 girls and 1 boy is 352 : (969 – 352) or 352
: 617.
4. ANS:
Let A represent the universal set of all model A cars.
Let L represent model A cars with heated leather seats.
Let S represent model A cars with a sunroof.
P(L  S) = 100% – 52%
P(L  S) = 48%
The probability of a model A car at a dealership having both heated seats and a sunroof is 29%.
5. ANS:
Let D represent the households that have one or more dogs, and let C represent the households that
have one or more cats.
P(D) = 29%
P(C) = 35%
P(D  C) = 100% – 42%
P(D  C) = 58%
P(C \ D) = P(C) – P(D  C)
P(C \ D) = 35% – 6%
P(C \ D) = 29%
The probability that a household has one or more cats, but no dogs, is 29%.
6. ANS:
There are 14 stuffed dogs and bears, and 36 other prizes. Therefore, the odds in favour of winning
either a stuffed dog or a stuffed bear are 14 : 36, or 7 : 18.
7. ANS:
P(W) = 40%
P(T) = 50%
P(W  T) = 10%
P(W  T) = P(W) + P(T) – P(W  T)
P(W  T) = 40% + 50% – 10%
P(W  T) = 80%
The probability that it will snow on Wednesday or on Thursday is 80%.