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Probability
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1. The local weather station reports that the chance of sleet is 0.99. Write this probability as a fraction and as a
percent.
a. 99 and 99%
c. 1 and 1%
100
b.
1
100
____
50
d.
and 1%
50
100
21
50
____
and 0.21
79
100
21
50
and 0.79
. Write this probability as a decimal and as a percent.
d.
5. What is the probability of rolling a number greater than 4 on a fair number cube?
a.
c.
d.
6. What is the probability of rolling a number less than or equal to 5 on a fair number cube?
a.
c.
b.
____
d.
a. 0.42 and 42%
c. 0.58 and 42%
b. 0.42 and 2.38%
d. 0.58 and 58%
4. A letter is chosen at random from the 26 letters in the alphabet. What is the probability of choosing a vowel?
a.
c.
b.
____
50
3. The chance that Rachel will win a prize is
b.
____
and 99%
2. Ross has a 79% chance of getting a black sticker out of a certain machine. Write this probability as a fraction
and as a decimal.
a. 21 and 0.21
c. 79 and 0.79
b.
____
99
d.
7. A local weather station forecasted a 93% chance of rain for the weekend. What is the probability that it will
not rain over the weekend?
a. 0.07%
c. 70%
b. 700%
d. 7%
____ 8. The probability of drawing a silver ball out of a certain bag is 0.3. What is the probability of not drawing a
silver ball?
a. 70
c. 0.07
b. 0.7
d. 0.77
____ 9. The probability of winning a prize at a school raffle is 0.62. What is the probability of not winning a prize at
the raffle?
a. 0.48
c. 3.8
b. 0.38
d. 38
____ 10. April has a blue dress, a purple dress, a white dress, and a yellow dress. For shoes, she can choose either dress
shoes, sandals, or slippers. How many different outfits can she wear?
a. 24
c. 12
b. 7
d. 14
____ 11. At a restaurant, Donald can choose between a roast beef sandwich, a chicken salad sandwich, and a fish
sandwich. As a side item he can choose apple slices, yogurt, or a salad. As a drink he can choose juice, water,
or tea. If he chooses one sandwich, one side item, and one drink, how many different meals can he choose
from?
a. 18
c. 27
b. 9
d. 12
____ 12. A middle school contains 6th, 7th, and 8th grade classes. One student from each grade will be chosen to
represent the school in an essay contest. The 6th grade finalists are Manuel, Sarah, Luis, and Eiko. The 7th
grade finalists are Benji, Eric, and Sandra. The 8th grade finalists are Hilda, Elizabeth, and Robby. How many
different ways can the students be chosen?
a. 27
c. 36
b. 10
d. 15
Greg spins the spinner twice.
2
5
3
4
____ 13. What is the probability that it will land on an even number both times?
a.
c.
b.
d.
____ 14. What is the probability that the spinner will land on 5 on the first spin and 2 on the second spin?
a.
c.
b.
d.
Mrs. Liang spins each spinner one time.
S pinner 1
6
9
S pinner 2
C
A
7
8
B
____ 15. What is the probability that the first spinner will land on an odd number and the second spinner will land on a
vowel?
a.
c.
b.
d.
____ 16. What is the probability that the first spinner will land on 7 and the second spinner will land on C?
a.
c.
b.
d.
Jared is going to perform an experiment in which he spins each spinner once.
S pinner 1
S pinner 2
A
1
4
B
S pinner 3
Blue Red
2
3
Green
____ 17. What is the probability that the first spinner will land on A, the second spinner will land on an even number,
and the third spinner will land on Blue?
a.
c.
b.
d.
____ 18. What is the probability that the first spinner will land on B, the second spinner will land on 3, and the third
spinner will land on Green?
a.
c.
b.
d.
Short Answer
19. There is a
chance that Sonia will have to wash the dishes tonight. Write this probability as a decimal and as
a percent. Show all of your work.
Essay
20. Explain a compound event and give an example.
Probability
Answer Section
MULTIPLE CHOICE
1. ANS: A
To represent the decimal as a fraction, multiply the decimal by 100, put the result over the denominator 100
and simplify. To represent the decimal as a percent, multiply by 100, and then add the percent symbol.
KEY: probability
NOT: /A/Correct! /B/Should you subtract the decimal from 1? /C/Is this the correct way to write the
probability as a fraction and as a percent? /D/Is this the correct fraction?
2. ANS: D
To represent a percent as a fraction, place the number over the denominator 100, and then simplify. To
represent a percent as a decimal, divide the number by 100.
KEY: probability
NOT: /A/This is the probability of NOT getting the given sticker. /B/Is this the correct way to write the
probability as a fraction and as a decimal?/C/Is this the correct fraction? /D/Correct!
3. ANS: A
To represent the fraction as a decimal, divide the numerator of the fraction by the denominator. To represent
the fraction as a decimal, divide, then multiply by 100 and add a percent symbol.
KEY: probability
NOT: /A/Correct! /B/Is this the correct percent? /C/Should you subtract the decimal from 1? /D/This is the
probability of NOT winning a prize.
4. ANS: D
There are 5 vowels in the alphabet of 26 letters. So the probability is
.
KEY: probability, theoretical probability
NOT: /A/Is this the probability of choosing a vowel or a consonant? /B/Should the number of possible
outcomes be in the top or bottom of the ratio? /C/Is the bottom of this ratio the number of possible outcomes?
/D/Correct!
5. ANS: A
There are six possible outcomes when a fair number cube is rolled. Because the number cube is fair, all
outcomes are equally likely. There are two numbers greater than 4 on the number cube: 5 and 6. So the
probability of rolling one of these numbers is
.
KEY: probability, theoretical probability
NOT: /A/Correct! /B/How many favorable outcomes are there? How many total outcomes are there? /C/Is
this the probability of rolling a number greater than or less than 4? /D/How many numbers greater than 4 are
there on a number cube?
6. ANS: A
There are six possible outcomes when a fair number cube is rolled. Because the number cube is fair, all
outcomes are equally likely. There are five numbers less than or equal to 5 on the number cube: 1, 2, 3, 4, and
5. So the probability of rolling one of these numbers is .
KEY: probability, theoretical probability
NOT: /A/Correct! /B/Is this the probability of rolling a number less than or less than or equal to 5? /C/Is this
the probability of rolling a number less than or equal to 5? /D/Is this the probability of rolling a number
greater than or less than 5?
7. ANS: D
Subtract the probability of the event’s occurring from 100%.
KEY: probability
NOT: /A/Should you move the decimal if you are still using the percent symbol? /B/Do you have to move
the decimal again? /C/Does the sum of this value and 93% add up to 100%? /D/Correct!
8. ANS: B
Subtract the probability of the event’s occurring from 1.
1 – 0.3 = 0.7
KEY: probability
NOT: /A/Should you move the decimal if you are not using the percent symbol? /B/Correct! /C/Does the sum
of this value and the probability of a silver ball add up to 1? /D/Does this value and the probability of drawing
a silver ball add up to 1?
9. ANS: B
Subtract the probability of the event occurring from 1.
KEY: probability
NOT: /A/Does this value and the probability of winning a prize add up to 1?/B/Correct! /C/Does the sum of
this value and the probability of winning add up to 1? /D/Should you move the decimal if you are not using
the percent symbol?
10. ANS: C
Make a tree diagram to organize the possible choices, and then count the number of choices.
KEY: probability, tree diagram
NOT: /A/Did you correctly organize the choices in the tree diagram? /B/Did you make a tree diagram to find
the number of outfits? /C/Correct! /D/Did you try making a tree diagram to help you find all the possible
outfits?
11. ANS: C
He has three choices to make and three options for each choice. Make an organized list to keep track of all the
different types of meals, and then count them.
KEY: probability, organized list, sample
NOT: /A/Did you correctly count the number of options for each choice? /B/Did you make an organized list
to find the number of meals? /C/Correct! /D/Did you try making an organized list to help you see the number
of meals?
12. ANS: C
Make an organized list to keep track of all the possible arrangements of students, and then count all of the
arrangements.
KEY: probability, organized list, sample
NOT: /A/Did you correctly count the number of finalists from each grade? /B/Did you make an organized list
to find the number of choices? /C/Correct! /D/Did you try making an organized list to help you see the
number of choices?
13. ANS: C
There are 16 possible outcomes, 4 of which have two even numbers.
(2, 2), (2, 3), (2, 4), (2, 5)
(3, 2), (3, 3), (3, 4), (3, 5)
(4, 2), (4, 3), (4, 4), (4, 5)
(5, 2), (5, 3), (5, 4), (5, 5)
The probability of spinning two even numbers is
= .
KEY: probability, compound events
NOT: /A/Did you count all of the possible ways that two even numbers could be spun? /B/Is there only one
way that two even numbers could be spun? /C/Correct! /D/Did you make a table to help organize all the
possible outcomes?
14. ANS: A
There are 16 possible outcomes. Of these, only 1 is spinning 5 first and 2 second.
(2, 2), (2, 3), (2, 4), (2, 5)
(3, 2), (3, 3), (3, 4), (3, 5)
(4, 2), (4, 3), (4, 4), (4, 5)
(5, 2), (5, 3), (5, 4), (5, 5)
The probability of spinning 5, then 2, is
.
KEY: probability, compound events
NOT: /A/Correct! /B/Does it matter in which order the two numbers are spun? /C/Did you make a table to
help organize all of the possible outcomes? /D/Is this only the probability that 5 will occur first?
15. ANS: D
There are 12 possible outcomes. Of these, 2 have an odd number first and an A second.
(6, A), (6, B), (6, C)
(7, A), (7, B), (7, C)
(8, A), (8, B), (8, C)
(9, A), (9, B), (9, C)
The probability of spinning an odd number, then a vowel, is
= .
KEY: probability, compound events
NOT: /A/Did you make a table to help organize all of the possible outcomes? /B/Did you correctly count the
number of ways this event occurred? /C/Did you include the first spinner's landing on an odd number in this
probability? /D/Correct!
16. ANS: D
There are 12 possible outcomes. Of these, only 1 is a 7 first and a C second.
(6, A), (6, B), (6, C)
(7, A), (7, B), (7, C)
(8, A), (8, B), (8, C)
(9, A), (9, B), (9, C)
The probability of spinning a 7, then a C, is
.
KEY: probability, compound events
NOT: /A/Did you make a table to help organize all of the possible outcomes? /B/Did you include the first
spinner's landing on 7 in this probability? /C/Did you include the second spinner's landing on C in this
probability? /D/Correct!
17. ANS: B
There are 24 possible outcomes. Of these, 2 have an A first, an even number second, and Blue third.
So, the probability of spinning “A, an even number, and Blue” is
=
.
KEY: probability, compound events
NOT: /A/Did you make a table to help organize all of the possible outcomes? /B/Correct! /C/How many even
numbers are on the second spinner? /D/Did you correctly count the number of ways this event occurred?
18. ANS: D
There are 24 possible outcomes. Of these, 1 has B first, 3 second, and Green third.
So, the probability of spinning “A, 3, and Green” is
.
KEY: probability, compound events
NOT: /A/Did you correctly count the number of ways this event occurred? /B/Did you make a table to help
organize all of the possible outcomes? /C/Can this event occur in more than one way? /D/Correct!
SHORT ANSWER
19. ANS:
0.4 and 40%
KEY: probability
ESSAY
20. ANS:
A compound event is an event made up of two or more single events. Suppose an experiment consists of
rolling a number cube, flipping a coin, and spinning a spinner that has the outcomes A, B, and C.
Then an example of a compound event would be rolling a 6, getting heads, and spinning a B, which can be
written as 6, H, B.
KEY: probability, compound events