Deck 10: Probability and Counting Techniques

Question 1

Which of the numbers that follow could represent a probability?

A)both I and II
B)neither
C)only II
D)only I

Answer 1

C

Question 2

In the game of rock, paper, scissors, two people play, and it's equally likely that you will win, lose,
Or tie. Find the probability of losing twice in a row.

A)
B)
C)
D)

Answer 2

C

Question 3

The difference between percent chance and probability is that we write probability as a number
between and .

Answer 3

zero; one

Question 4

Which of the numbers that follow could represent a probability?
I. 50% II. 35%

A)only I
B)neither
C)only II
D)both I and II

Question 5

If a die is rolled one time, find the probability of getting a number greater than 6.

A)1
B)5/6
C)0
D)1/6

Question 6

There are 75 balls in a bingo hopper. The ones numbered 1-15 are labeled with B, the ones from 16
-30 with I, from 31-45 N, from 46-60 G, and from 61-75 O. Find the probability of drawing a
Number less than 22.

A)
B)
C)
D)

Question 7

When an event can't possibly occur, its probability is . When an event is certain to occur, its
probability is .

Question 8

There are 75 balls in a bingo hopper. The ones numbered 1-15 are labeled with B, the ones from 16
-30 with I, from 31-45 N, from 46-60 G, and from 61-75 O. Find the probability of drawing I28.

A)0
B)
C)
D)

Question 9

For an event E in a sample space, the set of all outcomes that are not in E is called the of E.

Question 10

In a classroom, the students are 14 boys and 4 girls. If one student is selected at random, find the
Probability that the student is a girl.

A)
B)
C)
D)

Question 11

If you add the probabilities for every outcome in the sample space, the result is always .

Question 12

In the game of rock, paper, scissors, two people play, and it's equally likely that you will win, lose,
Or tie. Find the probability of losing at least once in two tries.

A)
B)
C)
D)

Question 13

The children at a certain school were asked what they prefer to drink with their lunch, and the
Following table summarizes the children's responses. The school only serves milk, chocolate milk, or water with lunch. What is the probability that the first student
In line for lunch will be served their preferred beverage with their lunch?

A)0.37
B)0.54
C)0.63
D)0.46

Question 14

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random,
What is the probability that it is not blue?

A)1/11
B)11/16
C)1/5
D)5/16

Question 15

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random,
what is the probability that it is green?

Question 16

In any experiment, the set of all possible outcomes is called the .

Question 17

If a die is rolled one time, find the probability of getting a number less than 4 or an even number.

A)1/6
B)1
C)5/6
D)0

Question 18

In the game of rock, paper, scissors, two people play, and it's equally likely that you will win, lose,
Or tie. Find the probability of having the same outcome twice in a row.

A)
B)
C)
D)

Question 19

There are 75 balls in a bingo hopper. The ones numbered 1-15 are labeled with B, the ones from 16
-30 with I, from 31-45 N, from 46-60 G, and from 61-75 O. Find the probability of drawing an odd
Number.

A)
B)
C)
D)

Question 20

There are 75 balls in a bingo hopper. The ones numbered 1-15 are labeled with B, the ones from 16
-30 with I, from 31-45 N, from 46-60 G, and from 61-75 O. Find the probability of drawing I10.

A)
B)
C)
D)0

Question 21

In December 2008, 500 men and 500 women were surveyed by Omnitel about their opinion on
whether federal government bailout money should be used to help homeowners in default. The
number giving each response is shown below. a. If a person who participated in the survey is selected at random, what is the probability that he or
she answered no?
b. What is the probability that the person selected is a man who answered either yes or no?
c. Based on the data from the survey, if you had stopped a random woman on the street in December
2008 and asked her opinion, what is the probability that she would have said that bailout money
should not be used to help homeowners in default?
d. Which type of probability (empirical or theoretical)are you using to answer these questions?
Explain.

Question 22

How many different ways can 3 winning tickets be selected from 50 tickets, without replacement, if
Each ticket wins a different prize? (Note: the tickets can be selected in any order.)

A)117,500
B)118,100
C)117,600
D)117,700

Question 23

Decide whether the selection described is a combination or a permutation.
Five club members are chosen to serve on a committee.

A)cannot be determined
B)combination
C)permutation

Question 24

A baseball pitcher has only three pitches: a fast ball, a curve ball, and a knuckle ball. As the pitcher
Warms up before an inning, she wants to throw a fast ball 2 times, a curve ball 6 times, and a
Knuckle ball 4 times. How many different ways can this be done.

A)48
B)13,860
C)9,979,200
D)12

Question 25

Decide whether the selection described is a combination or a permutation.
Three prizes are given to the winners of a race.

A)cannot be determined
B)combination
C)permutation

Question 26

Of the next 33 trials on the docket in a county court, 4 are homicides, 11 are drug offenses, 7 are
Assaults, and 11 are property crimes. If jurors are assigned to trials randomly, what's the probability
That a given juror won't get a property crime case?

A)
B)
C)
D)

Question 27

On The Price Is Right game show, to get into the showcase at the end, contestants spin a wheel with
20 equally sized spaces, numbered 5 cents, 10 cents, 15 cents, and so on, up to $1.00. If the
contestant spins once, find the probability of each event below.
a. $1.00
b. An amount less than 35 cents.
c. An amount greater than 70 cents.
d. An amount that is divisible by five.

Question 28

How many different ways can 3 people stand in line at a cash register?

Question 29

Evaluate 8!

Question 30

Evaluate the expression.

A)56
B)2
C)1
D)840

Question 31

How many different three letter permutations can be formed from the letters in the word clipboard?

A)336
B)544,320
C)729
D)504

Question 32

There were 7,234 single-bias hate crime offenses reported in a certain country in 2015. These crimes
were divided into categories, with the following breakdown: 3,264 were based on racial bias, 1,446
on religious bias, 1,411 on sexual orientation bias, 1,065 on ethnic bias, and 48 against those with
disabilities.
a. Make a frequency distribution for this data
Now use your frequency distribution to find the probability of each event in parts b-d.
b. Crime was motivated by sexual orientation bias.
c. Crime was motivated by bias against race or ethnicity.
d. Crime was not motivated by bias against religion or those with disabilities
e. Which type of probability (empirical or theoretical)are you using to answer these questions?
Explain.

Question 33

a. In how many ways can the letters in the word TEXAS be arranged?
B. In how many ways can the letters in the word OHIO be arranged?

A)
B)
C)
D)

Question 34

Evaluate .

Question 35

A babysitter has four lollipops of different colors. In how many ways can she give onelollipop to
each of the four children she is watching?

Question 36

Evaluate .

Question 37

Find both the number of combinations and the number of permutations for the given number
Of objects.
10 objects taken 7 at a time

A)
B)
C)
D)

Question 38

Evaluate the expression.
(4!)(3!)

A)144
B)479,001,600
C)30
D)5,040

Question 39

A 2-lb bag of Hershey's miniatures contains 35 milk chocolate bars, 26 Krackel bars, 29 Mr.
Goodbars, and 18 Special Dark bars. Set up a frequency distribution and find the probability that a
bar chosen from a randomly selected bag is
a. A Mr. Goodbar.
b. A Krackel or Special Dark.
c. Not a milk chocolate bar.
(Express your answers as decimal values rounded to three places)

Question 40

How many 3-digit codes using the digits 0 through 9 are possible if repetitions are allowed?

A)30
B)1000
C)504
D)729

Question 41

Three coins are tossed. Find the probability that no more than one coin lands heads up.

A)5/8
B)1/4
C)3/8
D)1/2

Question 42

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 2 or a king.

Question 43

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a black card.

Question 44

Two dice are rolled. Find the probability of getting a sum of 3 or 8.

Question 45

Three coins are tossed. Find the probability that two or more coins land heads up.

Question 46

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 4 of
Diamonds.

A)1/52
B)1/4
C)1/13
D)1/26

Question 47

Two dice are rolled. Find the probability of getting a sum of 6.

A)1/18
B)5/36
C)1/6
D)1/9

Question 48

How many ways can a person select four books, two CDs, and one DVD from ten books, twenty
CDs, and five DVDs?

A)8,000
B)199,500
C)405
D)6,724,520

Question 49

How many different ways can a college select three applicants for a teaching position from a pool of
20 applicants?

Question 50

Three coins are tossed. Find the probability that at least one coin lands heads up.

Question 51

Three coins are tossed. Find the probability that exactly two coins land tails up.

Question 52

Draw a tree diagram to determine the sample space when three coins are tossed.

Question 53

Three coins are tossed. Find the probability that all the coins land heads up

A)1/8
B)1/16
C)1/3
D)3/8

Question 54

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond
And an ace.

A)1/26
B)1/52
C)4/13
D)1/13

Question 55

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 7.

A)1/13
B)1/52
C)1/26
D)1/4

Question 56

How many ways can a committee of 3 people be selected from a group of 8 people?

Question 57

Four balls are numbered 1 through 4 and placed in a box. Two balls are selected without replacement.
Find the probability that
(a)the sum of the numbers is even.
(b)the number on the second ball is less than the number on the first ball.
(c)the sum of the numbers on both balls is greater than 3.

Question 58

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond or
A 10.

A)1/26
B)1/52
C)4/13
D)1/13

Question 59

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a red 6.

A)1/52
B)1/4
C)1/13
D)1/26

Question 60

A teacher has 20 boys and 10 girls in her class. In how many ways can she select 6 of the children
To be in a play if she must select 3 boys and 3 girls.

A)136,810
B)136,820
C)136,790
D)136,800

Question 61

Two dice are rolled. Find the probability of getting a sum less than or equal to 4.

Question 62

In a class of 20 students, there are 12 girls and 8 boys. Three students are selected to be teacher's
assistants. Find the probability that the group consists of one girl and two boys.

Question 63

Suppose that the probability of an female living in a particular country developing some type of
Cancer at some point in her life is about 1/7. Find the odds in favor of and against an American
Woman developing cancer.

A)In favor 1:8; against 8:1
B)In favor 6:1; against 1:6
C)In favor 1:6; against 6:1
D)In favor 8:1; against 1:8

Question 64

If the probability of event B is given by , then find the odds in favor of and against C.

A)In favor 6:19; against 19:6
B)In favor 19:6; against 6:19
C)In favor 7:6; against 6:7
D)In favor 6:7; against 7:6

Question 65

When a single card is drawn from a shuffled deck of cards, find the odds in favor of getting an ace.

A)1:12
B)51:1
C)1:51
D)12:1

Question 66

A package contains 15 candy canes, 13 of which are cracked. If 2 are selected, find the probability
Of getting exactly one cracked candy cane.

A)0.4513
B)0.5495
C)0.2476
D)0.3581

Question 67

Two dice are rolled. Find the probability of getting a 5 on one die or on both dice.

A)11/36
B)1/3
C)1/6
D)7/18

Question 68

In a class of 20 students, there are 12 girls and 8 boys. Three students are selected to be teacher's
assistants. Find the probability that the group consists of all girls.

Question 69

Find the probability of selecting 4 math books and 5 history books from a stack that contains 5 math
books and 9 history books if the books are selected at random.

Question 70

In one lottery game, contestants pick six numbers from 1 through 40 and have to match all six for
The big prize (in any order). What's the probability you'll win if you buy one ticket?

A)
B)
C)
D)

Question 71

When a single card is drawn from a shuffled deck of cards, find the odds against getting a 6.

A)1:12
B)12:1
C)1:51
D)51:1

Question 72

A person rolls two dice and wins if the sum is 7. What are the odds in favor of winning? What are
the odds against winning?

Question 73

To win a prize, a person must select 4 numbers from 15 numbers without replacement. Find the
Probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.)Round to four decimal places, if necessary.

A)0.2667
B)0.0007
C)0.0167
D)0.0022

Question 74

When two dice are tossed, find the odds against getting a sum of 8.

Question 75

Two dice are rolled. Find the probability of getting a sum greater than 8.

A)13/36
B)5/18
C)2/9
D)0

Question 76

If the probability of event B is given by , then find the odds in favor of and against B.

A)In favor 12:1; against 1:12
B)In favor 1:12; against 12:1
C)In favor 11:1; against 1:11
D)In favor 1:11; against 11:1

Question 77

A package contains 14 candy canes, 8 of which are cracked. If 3 are selected, find the probability of
Getting no cracked candy canes.

A)0.3568
B)0.0549
C)0.1654
D)0.2586

Question 78

Find the probability of randomly selecting three science books and four history books from a box
Containing five science books and six history books.

A)5/11
B)1/5
C)7/11
D)2/5

Question 79

When two dice are tossed, find the odds in favor of getting a sum of 7.

Question 80

Find the probability of getting any triple-digit number where all the digits are the same in a lottery
Game that consists of picking a three-digit number using the digits 1 to 8. Round to three decimal
Places, if necessary.

A)0.125
B)0.002
C)0.016
D)0.003