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Probability and Counting

Total questions: 100

Worksheet time: 3hrs 20mins

Name
Class
Date
1.
What is the probability of choosing a Honda? 
a)
.5970
b)
.5373
c)
.4627
d)
.4030
2.
Mary is a good student. The probability that she studies and passes her test is 3/5. If the probability that she studies is 8/9. What is the probability that she passes given that she studies? 
a)
27/40
b)
1.48
c)
.008
d)
.0593
3.
What is the probability that a student does play a sport given they do not play an instrument? 
a)
.2
b)
.2222
c)
.10
d)
.5
4.

A new credit card has been issued to 2000 customers. Of these customers, 1500 hold a Visa, 500 hold an AA card, and 40 hold a Visa and AA card. Find the probability that a random chosen customer holds an AA, given they hold a Visa.

a)

.0267

b)

37.5

c)

.02

d)

.3333

5.
What is the probability that the person picked will be a boy given they speak german? 
a)
.7273
b)
.4
c)
.16
d)
.22
6.

The probability that a woman likes the color blue is 10%. The probability of liking blue is 40%. What is the probability that a woman is chosen given they liked the color blue?

a)

4

b)

.4

c)

.1

d)

.25

7.
What is the probability that a female is chose given they like a Toyota? 
a)
.525
b)
.4627
c)
.6774
d)
.3143
8.
What is the probability that a student plays an instrument 
a)
.55
b)
.5
c)
.45
d)
.4
9.
What is the probability that they speak French given they are a girl? 
a)
2.14
b)
.24
c)
.4
d)
.8571
10.
What is the probability that a student plays on a sports team given they don't play an instrument? 
a)
.7273
b)
.8
c)
.55
d)
.2222
11.
What is the probability that a student does not play on a sports team? 
a)
.5
b)
.45
c)
.55
12.
Mary is a good student. The probability that she studies and passes her test is 3/5. If the probability that she studies is 8/9. What is the probability that she passes given that she studies? 
a)
27/40
b)
1.48
c)
.008
d)
.0593
13.
A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?
a)
3/10
b)
3/9
c)
1/9
d)
1/3
14.
P(Sandals|Pants):
a)
4/20
b)
6/15
c)
1/2
d)
2/7
15.

What proportion of senior boys play football or wrestle?

a)

9/143

b)

12/143

c)

18/143

d)

39/143

16.
How many senior boys play football but do not wrestle?
a)
9
b)
12
c)
18
d)
104
17.

How many senior boys play neither sport?

a)

9

b)

104

c)

30

d)

39

18.
What does the shaded portion of the Venn diagram represent?
a)
Not p
b)
p or q
c)
p and q
d)
Not q
19.
What does the shaded portion of the Venn diagram represent?
a)
Band and Art
b)
Only Art
c)
Band or Art
d)
Neither
20.

What is P(Foreign language | Sport)? (Remember to reduce the fraction!)

a)

14/27

b)

7/12

c)

23/47

d)

37/47

21.
What is the probability that the person picked will be a boy given they speak german? 
a)
.7273
b)
.4
c)
.16
d)
.22
22.
What is the probability that they speak French given that they are a girl? 
a)
2.14
b)
.24
c)
.4
d)
.8571
23.
What percentage of the days that it rained, did they forecast no rain?
a)
About 20%
b)
About 18%
c)
About 14%
d)
About 12%
24.

Is the probability of picking a white sock and picking a striped sock independent?

a)

Yes 2/5=2/5

b)

No 5/2=\=42/27

c)

Yes 27/42=27/42

d)

No 2/5=\=27/42

25.

What is the probability that a female plays sports

a)

39/334

b)

67/696

c)

39/696

d)

67/334

26.
According to Bayes' Theorem, P(A|B) =
a)
P(A and B)/[ P(A and B) + P(A' and B) ]
b)
P(A or B)/[ P(A or B) + P(A' or B) ]
c)
P(A and B)/[ P(A and B) + P(A and B') ]
d)
P(A and B)/[ P(A and B)  P(A' and B) ]⋅
27.
If P(A) = 0.20, P(B|A)=0.60 and P(B|A')=0.25, then P(A|B) = 
a)
0.3750
b)
0.7059
c)
0.6250
d)
0.2941
28.
A virus has infected 1.8% of a population. A test detects this virus 95% of the time when it is actually present, but it returns a false positive 3% of the time when the virus is not present.
If a person selected at random from this population tests positive for the virus, what is the probability that this person is actually infected? [Round to the nearest percent.]
a)
37%
b)
63%
c)
34%
d)
66%
29.
A witness claims that a black car was involved in a nighttime accident. Police know that, at night, witnesses identify black cars correctly 90% of the time, but 30% of the time misidentify cars of other colors as black.
If 8% of cars in the city are black, what is the probability that a black car really was involved in the accident?
a)
0.2069
b)
0.0845
c)
0.7931
d)
0.6200
30.
A rare species of dragonfly is always born with an extra set of wings. However, common dragonflies also sometimes get an extra set of wings through a mutation. 0.3% of dragonflies in a certain habitat belong to this rare species, and the extra-wing mutation is known to occur in 0.1% of common dragonflies.
You see a dragonfly in this habitat with an extra pair of wings. What is the probability that it is a member of the rare species?
a)
0.7506
b)
0.1003
c)
0.0004
d)
0.9996
31.
You think that there is about a 5% chance that ghosts exist. Then your uncle, whom you have never known to lie, says he saw a ghost. On the other hand, your uncle has poor eyesight and once mistook a bag of mulch for a dog.
Your estimate of the probability of ghosts existing should...
a)
Increase slightly
b)
Increase to 100%
c)
Decrease slightly
d)
Decrease to 0%
32.
Suppose that 5% of companies in a certain industry discriminate against Iowans. If a company discriminates, it will never hire someone from Iowa.
Suppose that 20 equally-qualified applicants apply for jobs at a company in this industry, and six are from Iowa. If this company hires four people from this set of applicants, but none are from Iowa, what is the probability that this company discriminates?
a)
0.2030
b)
0.7970
c)
0.5095
d)
0.4905
33.
A test returns a positive result for a virus 90% of the time when the virus actually is present. However, it also returns a positive result 8% of the time when the virus is not present.
0.1% of people in a certain population are infected with this virus. Is this test an effective way to search for this virus? Why or why not?
a)
Yes, 90% of people with the virus test positive.
b)
No, almost 99% of people with positive results do not have the virus.
c)
No, 8% of people without the virus test positive.
d)
Yes, 92% of people without the virus test negative.
34.
83% of a certain airline's flights depart on time. Of these flights, 90% also arrive on time. 30% of flights from this airline that depart late manage to make up time in the air to still arrive on time.
You see a flight from this airline arriving on time. What is the probability that it departed on time?
a)
0.9361
b)
0.9608
c)
0.9721
d)
0.8532
35.
Urn A contains three white and five black balls. Urn B contains two white and eight black balls.
I hand you one of these urns at random and you select a ball from that urn at random.
If that ball is white, what is the probability that I handed you Urn A? [Round to the nearest percent.]
a)
60%
b)
65%
c)
55%
d)
70%
36.
A meteorologist makes a forecast for rain or no rain every day, and she is 99% accurate in the following sense: If it rains on a given day, she predicted that it would rain on that day 99% of the time, and if it does not rain on a given day, she predicted no rain for that day 99% of the time.
Suppose however that this meteorologist lives in a desert where it only rains 3 days per year. If she predicts rain for this desert tomorrow, what is the probability that it actually will actually rain? [Ignore leap years.]
a)
99%
b)
45%
c)
55%
d)
97.2%
37.

Review: A store sells shirts that are either small, medium, or large. Each size comes in either yellow, red, blue or green. If a person selects from these choices at random, what is the probability that they will select a large green shirt?

a)

1/3

b)

1/7

c)

1/9

d)

1/12

38.

Review: A family has planned out game night for a whole school week (5 days.) They will let a six-sided die determine if they will play a board game or a card game. If the die lands on an even number, then they will play a card game and if it lands on an odd number, they will play a board game. What is the probability that they will play a board game every night of the week?

a)

0.03125

b)

0.1

c)

0.03333

d)

0.01667

39.

Review: A trial consists of drawing a card from a bag, and then drawing a second card without replacing the first.


Events in Sequence in the sample space for this trail are ______________ in relation to each other.

a)

Independent

b)

Dependent

c)

Disjoint

d)

Zero

40.

Review: Carlos wants to know the favorite sport of people at his school so he asks the 10 members of his baseball team. This survey is...

a)

Biased, because of who he asked

b)

Unbiased, because of who he asked

c)

Biased, because of how many people he asked

d)

Unbiased, because of how many people he asked

41.
A team of 8 basketball players needs to choose a captain and co-captain.
a)
64
b)
56
c)
15
d)
40,320
42.
A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
a)
200
b)
4.3609 x 1010
c)
0
d)
1,081,575
43.
A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there? 
a)
64
b)
14
c)
24,024
d)
2184
44.
You go to Best Buy to purchase a new television. You have the following choices: LCD or plasma; screen size 27”, 32”, 36”, 41”, 51”, or 63” and manufacturer Sony, Vizio or Phillips. How many different televisions does the store have to offer? 
a)
18
b)
990
c)
72
d)
36
45.
A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.
a)
135
b)
85,140
c)
14,190
d)
91,125
46.
5 out of 13 students will ride in a car instead of a van
a)
1,287
b)
154,440
c)
371,293
d)
65
47.
There are 45 applicants for three Computer Programmer positions.
a)
135
b)
85,140
c)
14,190
d)
91,125
48.
A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there?
a)
40
b)
5040
c)
6561
d)
10,000
49.
A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there if you cannot reuse a number?
a)
40
b)
5040
c)
6561
d)
10,000
50.
When does the order in which you are choose matter?
a)
Combination
b)
Permutation
51.
When does the order in which you are choose not matter?
a)
Combiniation
b)
Permutation
52.
What is the formula for Combinations?
a)
n!∕(n-r)! r!
b)
n!∕(n-r)!
c)
r!∕(r-n)! n!
d)
n!
53.
What is the formula for Permutations?
a)
n!
b)
n!∕(n-r)!
c)
n!∕(n-r)! r!
d)
r!∕(r-n)! n!
54.
What is the r value for choosing 5 cards from a standard deck of cards? 
a)
2
b)
5
c)
13
d)
52
55.
How many ways can 8 cheerleaders be chosen for 3 positions on the cheer team?
a)
24
b)
56
c)
128
d)
336
56.
How many ways can 9 runners medal (Gold, Silver or Bronze) in a race?
a)
27
b)
84
c)
216
d)
504
57.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does A∩¬B mean
a)
You don't clean your room and take out the trash.
b)
You clean your room or take out the trash
c)
You clean your room and take out the trash
d)
You clean your room but didn't take out the trash
58.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does A∪¬B
a)
You clean your room or don't take out the trash
b)
You don't clean your room or take out the trash
c)
You clean your room and take out the trash
d)
You clean your room or take out the trash
59.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does ¬(A∩B) mean?
a)
You don't do one of your chores
b)
You don't do either of your chores
c)
You clean your room but take out the trash
d)
You don't clean your room but take out the trash
60.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does ¬(A∪B)
a)
You don't do both of your chores
b)
You don't do at least one of your chores
c)
You don't clean your room but take out the trash
d)
You clean your room but don't take out the trash
61.
You flip a coin three times. What is the probability of three consecutive heads?
a)
½
b)
⅓
c)
⅙
d)
⅛
62.
Which answer describes conditional probability  
a)
A conclusion drawn  based on what one 
already knows and 
on that alone
b)
The probability of 
some event A,
 assuming event B
c)
The number of 
favorable outcomes 
divided by 
the total number of 
possible outcomes.
d)
The occurrence of some 
event A automatically
implies the non–occurrence of a 
second event B.
63.
Jim draws 4 cards from a deck of cards.  What is the probability of all 4 cards being clubs?
a)
13C4
52P4
b)
13C4
52C4
c)
1
52C4
d)
1
52P4
64.
Eight racers are running and Tom wants to know his probability to earn a medal (Gold, Silver or Bronze).
a)
⅓
b)
⅗
c)
⅜
d)
⅝
65.
James purchased 3 shirts, 3 jackets and 2 pairs of pants.  How many different outfits using a shirt, a jacket, and pants are possible?
a)
8
b)
18
c)
54
66.
The value of 5! is ____.
a)
25
b)
15
c)
120
d)
720
67.
Which of the following would you use to calculate the number of ways to elect a President, a Vice President, and a Secretary from a group of 12 individuals. Think: Does order matter?
a)
Permutation
b)
Combination
c)
Neither
68.
What does 10C5 mean?
a)
Combinations with 5 choices and 10 positions
b)
Combinations with 10 choices and 5 positions
c)
Permutations with 5 numbers and 10 operations
d)
Permutations with 5 hot dogs and 10 drinks
69.
What is the value of 5P2?
a)
60
b)
10
c)
20
d)
15
70.
How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits? Think: Does order matter?
a)
90
b)
100
c)
12
d)
24
71.
Which of the following would be used to calculate the number of ways one could choose 3 toppings for a sundae out of a list of 15?
a)
Permutation
b)
Combination
c)
Neither
72.
A team of 17 volleyball players needs to choose three players to refill the water cooler.  How many different ways can the players be chosen?  
a)
3360
b)
560
c)
4080
d)
680
73.
Ambry must submit 4 paintings as part of her application to art school. If she has 25 to choose from, how many ways can she pick 4? Think: Does order matter?
a)
12,650
b)
303,600
c)
100
d)
254
74.
What is the formula for combinations?
a)
n!∕(n-r)! r!
b)
n!∕(n-r)!
c)
r!∕(r-n)! n!
d)
n!
75.
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
76.

How many ways can you arrange 10 books on a shelf?

a)

10

b)

100

c)

50

d)

3,628,800

77.

How many different arrangements can be made from WATER?

a)

5

b)

120

c)

10

d)

0

78.

How many different arrangements can be made from MATH?

a)

10

b)

0

c)

6

d)

24

79.

How many different arrangements can be made from COLLEGE?

a)

28

b)

720

c)

5040

d)

35280

80.

How many ways could you choose 2 different letters from PROBABILITY?

a)

3,628,800

b)

28

c)

55

d)

403,200

81.

Simply the expression: 9P4

a)

36

b)

120

c)

35

d)

3024

82.

A(n) ______ is a list of all possible outcomes that may occur.

a)

sample space

b)

event

c)

outome

d)

counting principle

83.

A single coin is flipped 7 times. How many different outcomes are possible?

a)

14

b)

128

c)

49

d)

823,543

84.

The fundamental counting principle states that if you wish to find the number of outcomes for a given situation, simply ___ the number of possible outcomes for each step of the event.

a)

add

b)

subtract

c)

multiply

d)

divide

85.

Suppose you are dealt three cards from a standard deck of 52 cards. How many different outcomes are possible for what your three cards might be?

a)

132,600

b)

140,608

c)

124,800

d)

156

86.

Noah's wallet contains a $1 bill, a $5 bill, and a $10 bill. If Madie takes two bills from his wallet (without replacing any), how many different outcomes are possible?

a)

6

b)

4

c)

8

d)

9

87.

How many 4 letter permutations can be formed from the letters in the name jayci?

a)

64

b)

24

c)

120

d)

32

88.

A ____ is a specific order or arrangement of a set of objects or items in which order DOES matter.

a)

permutation

b)

combination

89.

A ____ is a specific order or arrangement of a set of objects or items in which order does NOT matter.

a)

permutation

b)

combination

90.

In how many different ways can 3 raffle tickets be selected from 20 tickets if each of the 3 ticket holders wins a different prize?

a)

6,840

b)

402,460

c)

32,064

d)

12,300

91.

Suppose there are 8 girls and 11 boys in the Junior class. How many ways can 3 girls and 4 boys be selected for a volleyball team?

a)

18,480

b)

386

c)

720

d)

2,460

92.

Suppose there are 12 students in the Statistics class. Mrs. Colwell selects 4 students to go home early. In how many ways can she do this?

a)

495

b)

11,880

c)

20,736

d)

16,777,216

93.

In how many ways can the letters in the word 'Kane' be arranged?

a)

8

b)

16

c)

24

d)

32

94.

How many different seating arrangements are possible for our stats class of 10 students?

a)

1,000,000,000

b)

2,800,300

c)

12,300,064

d)

3,628,800

95.

Which of the following is NOT an organizational strategy used in statistical counting methods.

a)

sets/lists

b)

tables/grids

c)

tree diagrams

d)

pictograms

96.

The cafeteria decides to allow students some options at lunch. Students may choose either milk or juice, chicken, pork, or steak, and potatoes or rice. How many different lunch combinations exist is a student is to pick 1 drink, 1 meat, and 1 side item?

a)

8

b)

6

c)

9

d)

12

97.
Which of the following situations is represented by this tree diagram?
a)
3 shirt options, 6 pants options, and 12 shoe options
b)
3 shirt options, 2 pants options, and 2 shoe options
c)
2 shirt options, 3 pants options, and 1 shoe option
98.
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
99.
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
100.

Which of the following is an example of combination?

a)

Form a passcode with 4 digits

b)

Students line up in a queue to assembly

c)

Choose 4 students in a class committee

d)

Choose the chairperson, secretary and treasurer in a club

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