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Applications of Math 12
Probability Review
Block
1. Determine which of the following events are independent:
a
b
The experiment is rolling a pair of dice. The first event is rolling an odd
number on one die and the second event is rolling an even number on the
other die.
The experiment is dealing two cards from a standard deck without
replacement. The first event is that the first card is a diamond and the second
event is that the second card is a diamond.
a. a only
b. b only
c. a and b
d. neither a nor b
2. A summary of a recent survey is shown below:
60% liked hamburgers, 70% liked pizza, 40% liked both
What percentage liked neither?
a. 10%
b. 20%
c. 30%
d. 40%
3. Moving only to the right or down along the dotted lines, how many different routes
exist to get from point A to point B?
a. 5
b. 6
c. 7
d. 8
4. There are 4 roads between cities A and B, and 3 roads between cities B and C. How
many ways can a person make a round trip from A to C by way of B without
travelling any road twice?
a.
b.
c.
d.
36
48
72
144
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
5. Assuming equally likely probabilities for male and female births, what is the
probability that a four-child family will have at least one boy?
a.
b.
c.
d.
1
16
1
8
7
8
15
16
6. In an experiment, two regular dice are rolled. Event A represents rolling the same
number on each die {doubles}. How many outcomes in the total sample space
represent the complement, A ?
a.
b.
c.
d.
6
12
24
30
7. How many different 10-digit telephone numbers can be created if the area code (first
three digits) is either 250 or 604 and the exchange (second three digits) is either 531,
535 or 540?
a.
b.
c.
d.
50 000
60 000
80 000
90 000
8. The diagram below shows a partial map of a certain city park, with walking paths
located on the grid lines.
A tourist starts at point A and randomly selects
a path to point C, walking only to the south and
east. What is the probability the tourist passes
through point B?
a.
b.
c.
d.
3
10
2
5
1
2
3
5
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
9. Companies A, B and C are bidding on a contract. From past records, it is known that
companies A and B are equally likely to get the contract, while company C has half
the likelihood of either A or B. What is the probability that company C will get the
contract?
a.
b.
c.
d.
0.20
0.25
0.30
0.40
10. How many different paths are there that reach from the top to exit 4?
a. 15
b. 16
c. 19
d. 20
11. A biased die was rolled 900 times, and the number 4 occurred 250 times. What is the
experimental probability of a 3 occurring?
a.
2
450
b.
1
6
c.
1
4
d.
2
125
e.
5
18
12. In the game “sandwich” three cards are dealt from a deck of 52 cards. To win, the
value of the 3rd card must be between the first two cards. What is the probability of
winning given the first two cards dealt are a 6 and a 10?
a.
8
25
b.
6
25
c.
3
13
d.
3
50
e.
4
13
13. There are 45 multiple-choice questions on an exam with 4 possible answers for each
question. How many different ways are there to complete the test?
a.
b.
c.
d.
45
148 995
3 575 880
4 45
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
14. Two dart players each throw one dart at a target. The probability of each player
hitting the bullseye is 0.3 and 0.4 respectively. What is the probability that both of
them will hit the bullseye? Assume independence.
a. 0.12
b. 0.35
c. 0.58
d. 0.70
15.Which of the following could not be the probability of an event happening?
a.
b.
c.
d.
½
0
1
-¾
16. In a raffle, 500 tickets were sold. What is the probability of winning if you purchased
10 tickets?
a.
b.
c.
d.
1
500
1
50
1
5
1
2
17. One card is drawn from a deck of well-shuffled cards. What is the probability that
the card is a diamond?
a.
b.
c.
d.
1
52
12
52
1
2
1
4
18.Which of the events below are dependent?
a.
b.
c.
d.
draw an ace from a deck and then another ace if the 1st card is replaced
roll a 6 on a die and roll a 5 on the same die
draw the number 2 out of a hat and then a 3 out of the same hat
draw the number 2 out of a hat and then a 3 if the 1st number is replaced.
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
19.A bag contains 3 red balls and 3 white balls. The first draw is a red ball and it is not
replaced. What is the probability that the 2nd draw will produce another red ball?
a.
b.
c.
d.
1
2
1
3
2
5
1
6
Use the following diagram to answer questions 20, 5 and 6
20.What is the total number of pathways from Charlene to Laura?
a.
b.
c.
d.
25
38
56
69
21.What is the probability of the ball landing in bin A?
1
5
a.
b.
c.
1
16
d.
1
32
1
8
A B C D E F
22.Which bin is the ball most likely to land in?
a.
b.
c.
d.
B
C
E
F
23.The probability that a student completes her Math assignment is 103 . The probability
that she completes her English assignment is 54 . What is the probability that she
finishes both assignments? Assume the events are independent.
a.
b.
c.
d.
6
25
7
15
1
2
4
5
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
24. 35% of the voters in the region are NDP’ers. If 4 voters are selected at random,
determine the probability that all 4 voted NDP.
a.
b.
c.
d.
1.5%
1.4%
4%
7%
25. A six-sided die is rolled 4 times. What is the probability that a 2 will be rolled at least
once?
a.
b.
c.
d.
0.67
3.33
0.52
0.48
26. Which of the events below are not mutually exclusive?
a.
b.
c.
d.
drawing a card that is a heart or a spade
drawing a card that is a ace or a face card
drawing a card that is a heart or a face card
drawing a card that is red or a club
Use the following situation to answer questions 27 & 28.
Numbers from 1 to 10 (inclusive) are placed in a hat. One number is selected at random.
27.Find the probability that the number is either less than 4 or greater than 6
a.
b.
c.
d.
3
25
7
10
49
100
1
10
28.Find the probability that the number is odd or greater than 7.
a.
b.
c.
d.
3
20
4
5
7
10
13
20
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
WRITTEN RESPONSE (Show your work)
1. A checkerboard is an 8
only diagonally on the dark squares, one diagonal square at a time, and only in a
downward direction. If a checker is placed as shown, how many possible paths are
there for the checker to reach the opposite side of the game board?
2. 2 six sided dice are rolled. Create a sample space that shows all the possible sums.
Die1/Die 2
1
2
3
4
5
1
2
3
4
5
6
a. Find the probability that the sum is less than or equal to 6.
b. Find the probability that the sum is less than 4 or greater than 9.
c. Find the probability that the sum is less than 9 or greater than 6.
Answer Key:
1A, 2A, 3B, 4D, 5D, 6D, 7B, 8A, 9A, 10D, 11E, 12B, 13D, 14A, 15D, 16B, 17D, 18C, 19C, 20D, 21D, 22B, 23A, 24A, 25C, 26C, 27B, 28C
1.
There are 69 paths to the other side in total
2.
15/36, 9/36, 11/36
6