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Worksheets

Theoretical Probability

Total questions: 123

Worksheet time: 11hrs 45mins

Name
Class
Date
1.

What is the probability of flipping a coin, getting tails?

a)

1/2

b)

1/3

c)

1/4

d)

Never, Tails never fails.

2.

What is the probability of spinning an even number?

a)

30%

b)

33%

c)

50%

d)

67%

3.

What is the probability of spinning yellow?

a)

1/11

b)

1/12

c)

1/4

d)

3/4

4.

Roll dice: 1, 2, 3, 4, 5

What is the probability of rolling a number greater than 2?

a)

3/5

b)

4/5

c)

2/5

d)

1/5

5.

If you choose from the following M & M colors, what is the probability that you choose blue? **Remember to simplify**

5 green

6 yellow

8 blue

7 brown

a)

8/18

b)

4/13

c)

8/25

d)

1/3

6.

A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a lemon?

*Remember to simplify*

a)

3

b)

1/10

c)

3/10

d)

30%

7.

You pick a marble from this bag.

What is the probability you will choose either a black or white marble?

a)

3/5

b)

9/100

c)

1/10

d)

2/5

8.
Find the theoretical probability of NOT landing on yellow if you spin the spinner.
a)
1/8
b)
7/8
c)
1
d)
7
9.
A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a quarter?
a)
5/11
b)
5/6
c)
1/3
d)
5
10.

What is the probability of spinning an odd number?

a)

3/6

b)

1/2

c)

1/3

d)

1/6

11.

What is the probability of spinning a red?

a)

1/5

b)

2/5

c)

1/2

d)

1/4

12.

If you choose from the following M & M colors, what is the probability that you choose brown? **Remember to simplify**

5 green

6 yellow

8 blue

7 brown

a)

7/26

b)

4/13

c)

8/25

d)

1/3

13.
What is the Theoretical Probablility of landing on red?
a)
43%
b)
33.3%
c)
40%
d)
36%
14.
What is the Theoretical Probability of not landing on red?
a)
25%
b)
50%
c)
65%
d)
66.7%
15.

A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a dime?

a)

2/11

b)

5/6

c)

1/3

d)

5

16.
You spin the spinner. How many possible outcomes are there?
a)
4
b)
8
c)
1
d)
6
17.
Find the theoretical probability of landing on orange or red if you spin the spinner.
a)
0
b)
3/8
c)
2/8
d)
1/4
18.
An experiment consists of rolling a fair number cube. Find the theoretical probability of rolling a 3.
a)
1/6
b)
3/6
c)
1
d)
1/2
19.

Theoretical P(4)

a)

3/6

b)

1/6

c)

1/2

d)

4/6

20.

Theoretical P(Green or Red)

a)

2/6

b)

1/5

c)

2/5

d)

1/5

21.

A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a dime?

a)

2/11

b)

5/6

c)

1/3

d)

5

22.
An experiment consists of rolling a fair number cube. Find the theoretical probability of rolling an 8.
a)
0
b)
8/6
c)
4/3
d)
1/2
23.
What is the probability of selecting an orange candy?
a)
0%
b)
25%
c)
50%
d)
100%
24.
What is the theoretical probability of rolling a number less than 6 when rolling one six-sided die?
a)
1/5
b)
2/3
c)
5/6
d)
1/3
25.

You have a jar with the following marbles: 4 blue, 8 red, 2 green


You randomly choose one marble from the jar. Find the theoretical probability of choosing one red marble.

a)

47\frac{4}{7}

b)

814\frac{8}{14}

c)

43\frac{4}{3}

d)

811\frac{8}{11}

26.

Probability is a number that describes the...

a)

relationship between two sets of data.

b)

percent of change.

c)

distance around a figure.

d)

likelihood that an event will occur.

27.

The complement of an event A is the set of all outcomes in the sample space that are _______ in the outcomes of event A.

a)

Included

b)

Not included

28.
What is the probability of choosing a vowel from the alphabet?
a)
21/26
b)
5/26
c)
1/21
d)
7/21
29.

What is the probability of flipping a coin and getting heads?

a)

1/2

b)

1/3

c)

1/4

d)

Never, Tails never fails.

30.
Probability can be written as ...
a)
a fraction
b)
a decimal
c)
a percent
d)
all of the above
31.
The likelihood that an event will NOT occur is known as its - 
a)
complement
b)
sample space
c)
opposite
d)
trial
32.
What is sample space?
a)
All of the Outcomes
b)
What Will Happen
c)
What Can Happen
d)
What I want to Happen
33.

What is the complement of flipping a coin 20 times and landing on heads 11 times?

a)

P' = 1/10

b)

P' = 11/20

c)

P' = 9/20

d)

P' = 10/20

34.

What is the probability of it snowing 3 days out of the week?

a)

P = 4/7

b)

P = 2/7

c)

P = 5/7

d)

P = 3/7

35.

What is the complement of it snowing 3 days out of the week?

a)

P' = 4/7

b)

P' = 2/7

c)

P' = 5/7

d)

P' = 3/7

36.

What is the probability of choosing a red marble if there are 8 red marbles in a jar of 15?

a)

P = 3/15

b)

P = 7/15

c)

P = 8/15

d)

P = 15/8

37.

What is the complement of choosing a red marble if there are 8 red marbles in a jar of 15?

a)

P' = 3/15

b)

P' = 7/15

c)

P' = 8/15

d)

P' = 15/8

38.

How likely are you to roll a 1 on a regular die?

a)

P = 2/6

b)

P = 3/6

c)

P = 5/6

d)

P = 1/6

39.

How likely are you to NOT roll a 1 on a regular die? (Complement)

a)

P' = 2/6

b)

P' = 3/6

c)

P' = 5/6

d)

P' = 1/6

40.

How likely are you to choose a yellow marble out of a jar, if there are 6 blue, 2 red, and 4 yellow?

a)

P = 4/10

b)

P = 1/3

c)

P = 2/12

d)

P = 6/12

41.

A bag of candy contains 2 red, 4 yellow, and 4 green candies.


P(NOT red or yellow) =

a)

3/5

b)

1/5

c)

2/5

d)

4/5

42.

There are 14 girls and 12 boys in a class.


P(boy) =

a)

7/13

b)

6/13

c)

4/13

d)

12/25

43.

P(NOT even) =

a)

5/7

b)

1/7

c)

2/7

d)

4/7

44.

Drew has 5 black T-shirts, 2 purple T-shirts, and 1 orange T-shirt.


P(white) =

a)

25%

b)

100%

c)

0%

d)

50%

45.

Drew has 5 black T-shirts, 2 purple T-shirts, and 1 orange T-shirt.


P(NOT white) =

a)

25%

b)

100%

c)

0%

d)

50%

46.
The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than “A”? 
a)
2/7
b)
5/49
c)
5/7
d)
10/49
47.

What is the probability of spinning a purple on the following spinner?

a)

1

b)

1/3

c)

1/2

d)

3/3

48.

There are five marbles in a bag. Three are green and two are yellow. You draw a marble, do not replace it, and then draw another. What is the probability of choosing two yellow marbles one after the other?

a)

2/5

b)

1/10

c)

1/4

d)

2/7

49.
a)

25\frac{2}{5}

b)

245\frac{2}{45}

c)

125\frac{1}{25}

d)

15\frac{1}{5}

50.
Suppose a number cube is rolled twice. What is the probability that an odd number will show both times?
a)
1/3
b)
1/2
c)
1/6
d)
1/4
51.
What is the probability of tossing a coin four times and getting tails each time?
a)
1/16
b)
1/8
c)
1/2
d)
1/4
52.
A coin is tossed and a number cube is rolled. Find the probability,  P(heads and 7).
a)
1/14
b)
1/2
c)
0
d)
1/7
53.
A number cube is rolled and a coin is tossed. What is the probability of rolling a number greater than 4 and tossing tails?
a)
1/6
b)
1/3
c)
1/2
d)
1/4
54.
Ten cards numbered 1-10 are placed in a hat. What is the probability of randomly drawing a card with an even number then a card with a number greater than or equal to five if the first card is replaced?
a)
1/4
b)
2/3
c)
3/10
d)
3/5
55.
A marble bag contains 3 red marbles, 4 gray marbles, 6 white marbles, and 5 black marbles. What is the probability of randomly drawing a red marble and then a gray marble if the first marble is replaced?
a)
1/9
b)
1/27
c)
1/6
d)
2/9
56.
When randomly drawing from a standard deck of 52 playing cards, what is the probability of drawing a 9 four times in a row if the cards are not replaced?
a)
1/5,525
b)
1/270,725
c)
1/28,561
d)
1/4
57.
In a standard deck of 52 cards, what is the probability of drawing one ace after another ace on two draws (no replacing)?
a)
1/221
b)
1/4
c)
1/169
d)
1/13
58.
There are 4 white marbles, 6 red marbles, and 2 blue marbles. Once a marble is selected, it is not replaced. Find the probability of selecting 2 blue marbles.
a)
1/2
b)
1/36
c)
1/6
d)
1/66
59.
Given a standard deck of 52 playing cards, what is the probability of randomly drawing a 2 and then a 3 if the first card is not replaced?
a)
1/13
b)
4/663
c)
1/676
d)
1/169
60.
A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent?
a)
Independent
b)
Dependent
61.
Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble. Does the outcome of the first draw affect the outcome of the second?
a)
Yes
b)
No
62.
There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color?
a)
2/5
b)
1/21
c)
4/25
d)
1/7
63.
A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random one after the other without replacement, then what is the probability that both the pencils are purple?
a)
9/182
b)
5/182
c)
2/91
d)
10/91
64.
Determine if the following events are dependent or independent.
Anna flips a coin two times.
a)
Independent
b)
Dependent
65.
In a box there are 3 red pens, 2 green pens, and 1 blue pen. What is the probability of picking a red pen, not replacing it, and then picking a blue pen?
a)
1/2
b)
4/11
c)
1/10
d)
2/3
66.
There are 10 pens and 15 pencils in a box. If a student selects two of them at random, then what is the probability of selecting a pen and then a pencil?
a)
7/12
b)
1/2
c)
1/4
d)
11/12
67.
A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent?
a)
Independent
b)
Dependent
68.
Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble. Does the outcome of the first draw affect the outcome of the second?
a)
Yes
b)
No
69.
There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color?
a)
2/5
b)
1/21
c)
4/25
d)
1/7
70.
There are 2 violet balls and 4 pink balls in a bag. If two balls are drawn one after the other, then what is the probability of getting violet first and pink next, if the first ball drawn is replaced?
a)
1/3
b)
2/9
c)
1/6
d)
1/4
71.
There are 5 red roses, 3 yellow roses, and 8 white roses in a tray. If Stephanie picked 2 roses one after the other without replacing, then what is the probability of picking a white rose first and a red rose next?
a)
1/6
b)
5/6
c)
1/3
d)
2/3
72.
A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random one after the other without replacement, then what is the probability that both the pencils are purple?
a)
9/182
b)
5/182
c)
2/91
d)
10/91
73.
Two fair coins are tossed. What is the probability of getting at most one head? (Hint: Create a sample space)
a)
1/2
b)
3/4
c)
1/4
d)
1
74.
What is the probability of rolling an even number on the first roll of a number cube and rolling an odd number on the second roll?
a)
1/4
b)
1
c)
1/8
d)
1/2
75.
A box contains all the letters of the word U N D E R S T A N D. What is the probability of selecting an 'N' first and a 'D' next, if the first letter is replaced?
a)
3/50
b)
1/25
c)
1/10
d)
2/5
76.

What is the probability of rolling an even number on the first roll of a number cube and rolling an odd number on the second roll?


Are these events independent or dependent?

a)

Independent

b)

Dependent

77.
There are 10 pens and 15 pencils in a box. If a student selects two of them at random, then what is the probability of selecting a pen and then a pencil?
a)
7/12
b)
1/2
c)
1/4
d)
11/12
78.

If you flip a coin two times, is it independent or dependent probability?

a)

Independent

b)

Dependent

79.

If you draw out a red marble, keep it, then draw out a blue marble, is it independent or dependent probability?

a)

Independent

b)

Dependent

80.

If you flip a coin then roll a number cube, is it independent or dependent probability?

a)

Independent

b)

Dependent

81.

Is the event INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then without putting the first card back, she picks a second card at random.

a)

Independent

b)

Dependent

82.

If two events are independent, then the outcome of the first event does NOT affect the outcome of the second event.

a)

True

b)

False

83.
To find the probability you of an INDEPENDENT event... 
a)
Find the probability of event #1
b)
Find the probability of event #2
c)
Add the probability of both event #1 & event #2
d)
Multiply the probability of both event #1 & event #2
84.

What is the probability of picking a blue marble, putting it back in the bag, then picking a red marble? (leave answer in fraction form in lowest terms)

a)

9/49

b)

16/49

c)

12/42

d)

12/49

85.
An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream.  A customer gets to choose a cone and a type of ice cream.  How many different 1-scoop ice cream cones can a customer order? 
a)
34
b)
2
c)
3
d)
93
86.
If you roll a die then flip a coin, how many possible outcomes?
a)
2
b)
6
c)
12
d)
64
87.
If you roll two dice, how many possible outcomes?
a)
360
b)
1
c)
36
d)
12
88.
How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?
a)
15
b)
40
c)
80
d)
10
89.
A particular model at a New Car Dealership comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
a)
180
b)
23
c)
12
d)
60
90.
At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?
a)
32
b)
192
c)
40,320
d)
51,200
91.
How many styles of sneakers are possible if Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red?
a)
12
b)
7
c)
223
d)
64
92.
Find the total number of outcomes for picking a day of the week and a month of the year.
a)
19
b)
84
c)
60
d)
210
93.
At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
a)
180
b)
23
c)
12
d)
60
94.
At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?
a)
32
b)
192
c)
40,320
d)
51,200
95.

How many license plates consisting of three letters followed by three numbers are possible when no repetition is allowed?

a)

26 x 25 x 24 x 10 x 9 x 8 = 11232000

b)

26 x 26 x 26 x 10 x 10 x 10 = 17576000

c)

26 x 25 x 24 x 9 x 8 x 7 = 7862400

d)

26 x 26 x 26 x 9 x 9 x 9 = 12812904

96.

In how many different ways can 4 different books be arranged on the shelf?

a)

4 x 3 x 2 x 1 = 24

b)

4 x 4 x 4 x 4 = 256

c)

4 + 3 + 2 + 1 = 10

d)

4 + 4 + 4 + 4 = 16

97.

A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each has a main dish, a salad, and a dessert?

a)

5 x 3 x 4 = 60

b)

5 + 3 + 4 = 12

98.

Permutation or Combination: The student body of 30 students wants to elect a president, vice president, secretary, and treasurer.

a)

permutation

b)

combination

99.

Permutation or Combination: Rob and Micaela are planning trips to four countries this year. There are 5 countries they would like to visit. One trip will be one week long, another two days, another two weeks, and the other a month.

a)

permutation

b)

combination

100.

Permutation or Combination: A group of 40 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

a)

permutation

b)

combination

101.

Permutation or Combination: A group of 14 people need to take an elevator to the top floor. They will go in groups of seven. They are deciding who will take the elevator on its second trip.

a)

permutation

b)

combination

102.

Permutation or Combination: You are setting the combination on a four-digit lock. You want to use the numbers 3817 but don't care what order they are in.

a)

permutation

b)

combination

103.

Permutation or Combination: Jaidee and Amy are planning trips to four countries this year. There are 6 countries they would like to visit. They are deciding which countries to skip.

a)

permutation

b)

combination

104.

Permutation or Combination: Willie and Paul are planning trips to two countries this year. There are 10 countries they would like to visit. One trip will be one week long and the other two weeks.

a)

permutation

b)

combination

105.

solve the following permutation: Jacob and Eugene are planning trips to four countries this year. There are 14 countries they would like to visit. One trip will be one week long, another two days, another two weeks, and the other a month.

a)

24024

b)

20876

c)

1001

d)

4804

106.

solve the following permutation: Kayla and Chelsea are planning trips to three countries this year. There are 5 countries they would like to visit. One trip will be one week long, another two days, and the other two weeks.

a)

80

b)

10

c)

60

d)

85

107.

solve the following permutation: The student body of 40 students wants to elect a president, vice president, secretary, and treasurer.

a)

2479595

b)

2140140

c)

2193360

d)

4386720

108.

solve the following permutation: The batting order for ten players on a 12 person team.

a)

239018325

b)

239500800

c)

238985815

d)

66

109.

solve the following combination: Amanda and Jimmy are planning trips to four countries this year. There are 8 countries they would like to visit. They are deciding which countries to skip.

a)

70

b)

45

c)

280

d)

260

110.

solve the following combination: A group of 20 people are going to run a race. The top 9 finishers advance to the finals.

a)

83980

b)

819782656

c)

167960

d)

335920

111.

solve the following combination: Selecting which seven players will be in the batting order on a 9 person team.

a)

36

b)

30

c)

72

d)

18

112.

How would you solve?

From the 20 DVD's you purchased this past year, you plan to take five with you on vacation. How many different sets of five DVD's can you take?

a)

Permutation

b)

Counting Principles

c)

Factorial

d)

Combination

113.

How would you solve?

A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

a)

Permutation

b)

Combination

c)

Factorial

d)

Counting Principles

114.

How would you solve?

The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?

a)

Permutation

b)

Combination

c)

Factorial

d)

Counting Principles

115.

A disc jockey has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

a)

84

b)

504

c)

362,880

d)

6

116.
How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?
a)
90
b)
100
c)
12
d)
24
117.

Robin has five different pairs of shoes that match with 6 different pairs of socks. How many shoes-and-socks combinations can she make if she selects one pair of shoes and one pair of socks?

a)

11

b)

30

c)

120

d)

720

118.

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

a)

720

b)

120

c)

6

d)

20

119.

4 letters are chosen at random from the word RANDOMLY. In how many ways can this selection be made?

a)

24

b)

1680

c)

70

d)

40320

e)

438

120.

The ski club with ten members is to choose three officers for captain, co-captain and secretary. How many ways can those offices be filled?

a)

720

b)

120

c)

10!

d)

6

121.

ONOMATOPIA. Find the number of arrangements if all letters must be used.

a)

302,400

b)

10

c)

3,628,800

d)

3,020,400

122.

Rhea has 10 basketballs, each of a different colour. She only has time to shoot 5 hoops before going to bed. How many different arrangements can the balls be thrown into the hoops?

a)

252

b)

120

c)

30,240

d)

3,628,800

123.

A telephone number in a single area code is composed of 7 digits from 0 to 9. Determine the amount of phone numbers available in the 856 area code if the first digit cannot be 0 or 1.

a)

483,840

b)

604,800

c)

8,000,000

d)

10,000,000

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