Deck 4: Probability and Counting Rules

Question 1

A compound event consists of two or more outcomes or simple events.

Answer 1

True

Question 2

A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of ____________ probability.

Answer 2

empirical

Question 3

At Wassamatta University, 55.7% of the student body are males. Choose one student at random. What is the probability that the student is female?

A) 5.7%
B) 50%
C) 55.7%
D) 44.3%

Answer 3

D

Question 4

If two dice are rolled one time, find the probability of getting a sum of 6.

A)
B)
C)
D)

Question 5

The statement, "The probability that a certain sports team will win it's next game is about 60%," is an example of

A) classical probability.
B) empirical probability.
C) subjective probability.
D) a sample space.

Question 6

If there are 18 equally likely events, then the probability of the first one occuring is 1/18.

Question 7

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A)
B)
C)
D)

Question 8

What is the set of all possible outcomes of a probability experiment?

A) an outcome
B) the sample space
C) events
D) a Venn diagram

Question 9

How many possible outcomes would there be if three coins were tossed once?

A) 2
B) 4
C) 6
D) 8

Question 10

If the probability that it will rain tomorrow is 0.37, what is the probability that it will not rain tomorrow?

A) 0.37
B) 0.37
C) 0.63
D) 1.37

Question 11

If two dice are rolled one time, find the probability of getting a sum less than 5.

A)
B)
C)
D)

Question 12

Tree diagrams are useful for

A) illustrating the law of large numbers.
B) finding all possible outcomes in a probability experiment involving several steps.
C) showing that the outcome is the set of all possible sample spaces.
D) ordering outcomes from lowest to highest.

Question 13

If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond?

A)
B)
C)
D)

Question 14

What type of probability uses a knowledge of sample spaces as opposed to experiments to determine the numerical probability that an event will occur?

A) classical probability
B) conditional probability
C) empirical probability
D) subjective probability

Question 15

Classical probability was the first type of probability studied formally by mathematicians of the 17th and 18th centuries.

Question 16

If one tosses a coin enough times, the number of heads and tails will tend to "even out." This is an example of the law of ______________.

Question 17

If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability?

A) classical probability
B) conditional probability
C) empirical probability
D) subjective probability

Question 18

If a die were rolled, the event of getting an even number would be called a simple event.

Question 19

Find the probability of getting a number greater than 4 when a die is rolled one time.

A)
B)
C)
D)

Question 20

Two events are mutually exclusive if they cannot both occur.

Question 21

In a recent study, the following responses were obtained to the question, "Do you favor recycling in your neighborhood?"
If a response is picked at random, what is the probability that it came from a male or that it indicated no opinion regarding recycling?

A)
B)
C)
D)

Question 22

If a coin is tossed three times, the probability that the coin lands on heads at least one of those three times is 7/8.

Question 23

In a second grade class containing 12 girls and 9 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls?

A)
B)
C)
D)

Question 24

If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade?

A)
B)
C)
D)

Question 25

Given the following Venn diagram, which of the following equations could be used to calculate the probability of either event A, event B, or event C occurring.

A)
B)
C)
D)

Question 26

If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace?

A)
B)
C)
D)

Question 27

Given eight students, three of which are female, if two students are selected at random, without replacement, what is the probability that both students are female?

Question 28

An apartment building has the following distribution of apartments: If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor?

A)
B)
C)
D)

Question 29

A probability experiment has two steps. There are two possible results for the first step, call them "A" and "B". If the result for the first step was "A", then there would be 4 possible results for the second step. If the result for the first step was "B", then there would be 15 possible results for the second step. How many possible outcomes are there for this experiment?

A) 60
B) 9
C) 15
D) 19

Question 30

In a fish tank, there are 23 goldfish, 4 angelfish, and 9 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy.

A)
B)
C)
D)

Question 31

The Statistics Club at Woodvale College sold college T-shirts as a fundraiser. The results of the sale are shown below. Choose one student at random. Find the probability that the student sold 11-15 T-shirts or less than 6 T-shirts.

A) 0.4444
B) 0.5278
C) 0.0833
D) 0.5429

Question 32

Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is first drawn from Box A and then another number from Box B. Using the figure below, how many outcomes are possible if both numbers are even?

A) 16
B) 4
C) 6
D) 8

Question 33

If a card is drawn from an ordinary deck of cards, and then a second card is drawn from the same deck without replacing the first card, these two events are ________________.

Question 34

At a certain college, there were 600 science majors, 200 engineering majors, and 500 business majors. If one student was selected at random, the probability that the student is an engineering major is

A)
B)
C)
D)

Question 35

A recent poll found that 30% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that all three will be worried about aggressive drivers on the road?

A) 0.900
B) 0.027
C) 0.081
D) 0.300

Question 36

A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, the probability that it is white or black would be .

Question 37

A single card is drawn from a deck. Find the probability of selecting a heart or a 9.

A)
B)
C)
D)

Question 38

According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 4 adults at random. The probability that all of them enjoy drinking beer is:

A) 0.250
B) 3.200
C) 0.200
D) 0.410

Question 39

A coin is tossed 5 times. Find the probability that all 5 tosses are tails.

A)
B)
C)
D)

Question 40

An apartment building has the following distribution of apartments:
If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?

A)
B)
C)
D)

Question 41

It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph?

Question 42

How many different ways can 5 brands of soda be displayed on a supermarket's shelf, one at a time in a row?

A) 10
B) 120
C) 240
D) 360

Question 43

A store manager wants to display 4 different brands of toothpaste in a row. How many ways can this be done?

A) 4
B) 12
C) 6
D) 24

Question 44

Urn 1 contains 6 red balls and 4 black balls. Urn 2 contains 4 red balls and 6 black balls. Urn 3 contains 4 red balls and 5 black balls. If an urn is selected at random and a ball is drawn, find the probability it will be red.

A)
B)
C)
D)

Question 45

A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?

A) 0.0264
B) 0.0531
C) 0.0347
D) 0.0482

Question 46

In the Happy Hilltop Health Home, 10% of the residents play shuffleboard, 35% of the residents play poker, and 10% of the residents garden. If 5% of the residents play poker and garden, find the probability that a resident plays poker, given that they also garden.

A) 50.0%
B) 14.3%
C) 5.6%
D) 7.7%

Question 47

Below are listed the numbers of engineers in various fields by sex. Choose one engineer at random. Find .

A) 0.787
B) 0.215
C) 0.152
D) 0.141

Question 48

Two events A and B are ______________ if the fact that A occurs does not affect the probability of B occurring.

Question 49

When the outcome of event A does not affect the probability of the outcome of a subsequent event B, then the events are said to be dependent.

Question 50

In a physics class there are 10 juniors and 20 males; so there must be 30 male juniors in this class.

Question 51

The ______________ probability of an event B in relationship to an event A is defined as the probability that event B occurs after event A has already occurred.

Question 52

When two events are independent, the probability of both occurring is:

A)
B)
C)
D)

Question 53

In a second grade class containing 13 girls and 9 boys, 2 students are selected at random to give out the math papers. What is the probability that the second student chosen is a boy, given that the first one was a girl?

A)
B)
C)
D)

Question 54

A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is , and the probability of selecting a blue chip on the first draw is , find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip.

A)
B)
C)
D)

Question 55

There are __________ possible ways that eight pictures can be hung along a wall.

Question 56

If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?

A) 625
B) 720
C) 7,776
D) 1,296

Question 57

There are 3 blue balls, 5 red balls, and 4 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one was white?

A)
B)
C)
D)

Question 58

On an eight-question true-false quiz, a student guesses each answer. What is the probability that the student gets at least one of the answers correct?

Question 59

A group of 10 male and 8 female students is talking about going out for pizza. If 50% of the male students actually go and 25% of the female students actually go, find the probability that a random student who goes out for pizza is female.

A)
B)
C)
D)

Question 60

There are 3 first grade children, 5 second grade children, and 6 third grade children in a room. When choosing two children, what is the conditional probability of choosing a second grade child, given that either a first or a third grade child was chosen first?

A)
B)
C)
D)

Question 61

There are four instructors, nine assistant professors, and five associate professors in the Math department. A committee of five is selected to choose new textbooks. There are 1,440 ways that a committee can be selected, if there must be one instructor, two assistant professors, and two associate professors on the committee.

Question 62

A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?

A) 5,040
B) 210
C) 840
D) 420

Question 63

Evaluate the following: ₇P₃.

A) 210
B) 35
C) 5,040
D) 6

Question 64

There are 3 different mathematics courses, 5 different science courses, and 2 different history courses. If a student must take one of each, how many different ways can this be done?

A) 10
B) 12
C) 30
D) 60

Question 65

If a menu has a choice of 4 appetizers, 4 main courses, and 4 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert ?

A) 64
B) 20
C) 32
D) 3

Question 66

is equal to 84.

Question 67

is equal to 84.

Question 68

There are 2,368 possible ways that a committee of eight people can be selected from a group of 14 people.

Question 69

A club has 10 members. There are 720 ways that a chairperson, a secretary, and a treasurer can be selected from these 10 members. Assume a person can hold, at most, one office.

Question 70

When a die is rolled twice, there are __________ possible outcomes.

Question 71

FizzFizz soda comes in two varieties, regular and diet. If a researcher has 4 boxes of each, how many ways can he select 2 boxes of each for a quality control test?

A) 36
B) 24
C) 15
D) 8

Question 72

How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together?

A) 24
B) 12
C) 6
D) 18

Question 73

A furniture manufacturer offers bookcases in 3 different sizes and 4 different colors. If every color is available in every size, then the total number of different bookcases is

A) 4
B) 7
C) 12
D) 24

Question 74

Evaluate the following: ₇C₃.

A) 210
B) 5,040
C) 35
D) 6

Question 75

A certain system has two components. There are 9 different models of the first component and 12 different models of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different sets of components can the salesman take?

A)
B)
C)
D)

Question 76

How many ways can a student select five questions from an exam containing 12 questions, if one of the five must be the last question?

A) 330
B) 7920
C) 40,320
D) 95,040

Question 77

Each of 8 students wishes to buy a particular textbook, but only 5 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?

A)
B)
C)
D)

Question 78

How many different ways can a teacher select 5 students from a class of 19 students to each perform a different classroom task?

A) 11,628
B) 95
C) 1,395,360
D) 240,240

Question 79

The number of different arrangements of four pictures from a selection of ten pictures is 5,040.

Question 80

A group of 6 children are choosing colored pencils to draw a picture. Each child is allowed to select one color. The available colors are green, red, and blue. If the second child refuses to use red pencils and the third child refuses to use blue pencils, then how many ways are there for the children to choose pencils? Assume that there are 12 pencils available of each color, and different children are allowed to choose the same color.

A) 324
B) 36
C) 729
D) 243