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Chapter 3: Probability
Math 3201
Unit Portfolio
Multiple Choice
1.
Jennifer draws a card at random from a standard deck of 52 cards. What are the
odds in favour of drawing a heart?
A.
C.
2.
C.
B.
D.
4:1
1:4
1
5
B.
D.
3
7
1
8
5
8
B.
D.
3
8
7
8
17.23%
27.35%
B.
D.
22.61%
34.06%
53.07%
59.36%
B.
D.
57.14%
62.23%
Andy and Amy are playing a board game. They use a standard 6-sided die. If a player
rolls a sum greater than 9 or a multiple of 6 then the player gets a 50 point bonus.
What is the probability of rolling a multiple of 6?
A.
C.
9.
4:5
1:5
Four boys and three girls will be riding in a van. Two people will be selected to sit in
the front seat. What is the probability that there will be one boy and one girl?
A.
C.
8.
0.500
0.750
Nine boys and twelve girls have signed up for a trip. Only six students will be
selected to go on the trip. What is the probability that there will be an equal number
of boys and girls on the trip?
A.
C.
7.
B.
D.
In #5 what is the probability that there will be at least one head?
A.
6.
0.250
0.625
Jane tosses three coins. She wants to calculate the probability that at least one coin
will land as heads. Determine the number of “favourable” outcomes for this (i.e. how
many ways can there be at least one head).
A.
C.
5.
1:3
3:13
The weather forecast says that there is an 80% probability of rain tomorrow. What
are the odds against rain tomorrow?
A.
C.
4.
B.
D.
Jennifer draws a card at random from a standard deck of 52 cards. What is the
probability of drawing a diamond?
A.
C.
3.
3:1
1:1
1
18
1
6
B.
D.
1
9
1
3
What is the probability of getting the 50 point bonus?
A.
C.
1  1
9
6
1  1
9
9
B.
D.
1  1
9
3
1  1
6
6
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Chapter 3: Probability
10.
C.
D.
16.3%
22.7%
B.
D.
18.4%
25.9%
1%
8%
B.
D.
5%
14%
2.42%
6.13%
B.
D.
3.33%
7.75%
There are 20 cards numbered 1 to 20 in a box. Two cards are drawn, one at a time,
with replacement. What is the probability of drawing an even number and then a
multiple of 4?
A.
C.
16.
0.4
0.6
A 5-colour spinner (Red, Blue, Yellow, Green, Purple) is spun and a standard 6sided die rolled. What is the probability of spinning yellow and rolling 6?
A.
C.
15.
B.
D.
Rachael goes to the gym and does two different workouts. The choices are the
treadmill, the stepper, the stationary bike, the elliptical walker, and running the
track. What is the probability that she will use the stepper and then the track?
A.
C.
14.
0.3
0.5
Rickie has 6 loonies, 4 toonies and 2 quarters in his pocket. He needs 2 loonies for
the meter. He takes 2 coins out of his pocket. What is the probability that they are
both loonies?
A.
C.
13.
Drawing a 7 or a heart from a deck of 52 cards
Rolling a sum of 4 or rolling an even number with a pair of 4-sided dice,
numbered 1 to 4.
Drawing a black card or drawing a queen from a standard deck of 52 cards
Rolling a sum of 8 or a sum of 11 with a pair of 6-sided dice numbered 1 to 6.
There are 40 males and 60 females in a graduating class. Of these 10 males and 20
females plan to attend university next year. What is the probability that a randomly
selected student plans to attend university.
A.
C.
12.
Unit Portfolio
Select the events that are mutually exclusive
A.
B.
11.
Math 3201
8.8%
10.7%
B.
D.
9.3%
12.5%
Select the dependent events
A.
B.
C.
D.
Rolling a 2 and rolling a 5 with a pair of 6-sided dice numbered 1 to 6.
Drawing an odd card from a standard deck of 52 cards, putting it back and
drawing another odd card
Drawing a spade from a standard deck of 52 cards, then drawing another
spade without replacing the first card
Rolling an even number and then rolling an odd number with a pair of 6sided dice numbered 1 to 6
17.
Select the independent events
A.
P(A) = 0.67 P(B) = 0.12 P(AB) + 0.086
B.
P(A) = 0.83 P(B) = 0.4 P(AB) = 0.378
C.
P(A) = 0.4 P(B) = 0.91 P(AB) = 0.364
D.
P(A) = 0.2 P(B) = 0.32 P(AB) = 0.046
18.
Two cards are drawn, without replacement, from a standard deck of 52 cards. What
is the probability of drawing a face card (Jack, Queen, King) then an even-numbered
card.
A.
C.
1.96%
14.32%
B.
D.
9.05%
23.08%
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Chapter 3: Probability
19.
20.
Math 3201
Unit Portfolio
Given the probabilities, which event is most likely to occur?
A.
P(A) = 0.28
B.
C.
P(C) = 27%
D.
P(B) = 1
4
P(D) = 1
5
The probability that Vince will study on Friday night is 0.7. The probability that he
will go out to dinner is 0.5. The probability that he will do at least one of these
things is 0.9. What is the probability that he will do both these things?
A.
C.
0.2
0.5
B.
D.
0.3
0.7
Constructed Response
21.
Paula needs to create a four-digit password to access her voice mail. She can repeat
some digits, but all four digits cannot be the same. What is the probability that that
the first digit of her password will be 7?
22.
Jessica draws a card from a standard deck of 52 cards. She then draws another card
without replacing the first card. What is the probability that both cards are red?
Write your answer to the nearest tenth of a percent.
23.
Jessica draws a card from a standard deck of 52 cards. She puts the card back and
then draws another card. What is the probability that both cards are black? Write
your answer to the nearest tenth of a percent.
24.
Jeff has been awarded a penalty shot in a hockey game. Jake is the goalie who has
blocked 6 of the last 11 penalty shots. What are the odds in favour of Jeff scoring?
25.
From a committee of 18 people, 3 are chosen at random to fill the positions of
president, vice-president, and secretary. Determine the probability to the nearest
hundredth of a percent that Haley, Holly and Hillary will be chosen.
26.
A hockey game ends in a tie. The winner is to be decided in a shootout. The coach
must decide between Julie and Jennifer. The coach wants to put the best scorer on
first, so the decisions is based on the players’ scoring records. Who should go first?
Explain your reason.
Player
Julie
Jennifer
Attempts
15
19
Goals Scored
7
12
Page 3 of 4
Chapter 3: Probability
Math 3201
Unit Portfolio
27.
Access to an online game site is password protected. Every player must create a
password that consists of 3 capital letters followed by 2 digits. Repetitions are not
allowed. What is the probability, rounded to the nearest thousandth of a percent,
that the chosen password will have the letters A, B and C, in any order.
28.
Alice has Scrabble tiles that spell the word CHAIRS. She has selected 3 of the tiles at
random. What is the probability, rounded to the nearest percent, that she selected
two consonants and one vowel.
29.
A student council consists of 12 girls and 8 boys. To form a sub-committee, 4
students are randomly chosen. Determine the probability that there will be at least
3 girls on the committee.
30.
If you draw a single card from a standard deck of 52 cards. Determine the
probability that you will draw out
a) a 7 or an ace
b) a black card or a face card
31.
There are 2 children in a family. Determine the probability that
a) both are girls
b) one is a boy and one is a girl
32.
Amanda has 4 tickets for a draw for 2 prizes. At the time of the draw 100 tickets
have been sold. The ticket that is drawn to win the first prize is returned for the
draw for second prize. Determine the probability that Amanda will
a) win both prizes
b) win no prizes
33.
Based on the soccer teams record, it has a 70% chance of winning on days without
rain and a 50% chance of winning on days with rain. The forecast for Friday
indicates a 20% chance of rain. What is the probability that the team will win on
Friday?
34.
A manufacturer knows that in a box of 120 light bulbs there will be 3 defective
bulbs. Ben picks 2 bulbs from a box of 120 bulbs. Determine the probability that he
will pick
a) 2 defective bulbs
b) exactly one defective bulb
35.
Amy draws a card at random from a standard deck of 52 cards. If she draws a face
card or a heart she wins.
a) Are the events mutually exclusive? Why? or Why not?
b) What is the probability that Amy will win a point?
Page 4 of 4