Introduction to Probability Unit Test Review and Test 100%

Evaluate the expression. 9!/3!

60,480

Consider the sets below. A {x|x is a polygon} B {x|x is a triangle} Which is true?

B ⊂ A

All freshmen, sophomores, juniors, and seniors attended a high school assembly. The total student attendance is shown in the table. Twice during the assembly, a student is chosen at random to assist with the presentation. After the first student has finished assisting, the student returns to the group and can be chosen a second time. What is the probability that the first student chosen is a senior and the second student chosen is a sophomore?

11/320

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen?

120

Under the best conditions, a sprout has a 40% probability of blooming. If two sprouts are selected at random, what is the probability that both will bloom, under the best conditions?

16 percent

The Venn diagram shows the number of patients seen at a pediatrician's office in one week for colds, C, ear infections, E, and allergies, A. How many patients had allergies or ear infections, but not both?

36

Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination. If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?

504

Carrie is finding the set of even numbers within the set of prime numbers. She starts by considering only positive numbers. Of the sets described, which is the universal set?

positive numbers

Pedro has determined that the probability his shot will score in a lacrosse game is 0.30. What is the probability that he will score on two consecutive shots?

0.09

A bag contains eleven equally sized marbles, which are numbered. What is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?

6/11

Two students from a group of eight boys and 12 girls are sent to represent the school in a parade. If the students are chosen at random, what is the probability that the students chosen are not both girls?

62/95

A farmer grows vegetables on seven acres, fruit on six acres, and flowers on two acres. Out in his fields, he finds a ladybug. To the nearest tenth of a percent, what is the theoretical probability that the ladybug was not found within the acres of flowers?

86.7%

Which sets can be represented using the Venn diagram below?

A = {animals}; B = {mammals}

Brent's after-school game club has 12 members from which a six-member team is created. Miguel's after-school sports club has 10 members from which a six-member team is created. Which student's club has more possible combinations for his six-member team?

Brent's club has more possible team combinations because there are more members to choose from.

Consider the following sets. U = {all triangles} E = {x|x ∈ U and x is equilateral} I = {x|x ∈ U and x is isosceles} S = {x|x ∈ U and x is scalene} A = {x|x ∈ U and x is acute} O = {x|x ∈ U and x is obtuse} R = {x|x ∈ U and x is right} Which is a subset of I?

E

Which events are independent? Check all that apply.

Roll a number cube, and then roll the same number cube again. Flip a coin, and then flip the coin a second time. Draw a card from a deck, replace it, and then draw a second card.

Consider a single spin of the spinner. Which events are mutually exclusive? Check all that apply.

landing on a shaded portion and landing on a 3 landing on an unshaded portion and landing on a number less than 2

The diagram shows the number of children who have ever used motorized scooters, manual scooters, and/or bicycles. Which combination represents the empty set?

motor ∩ bicycle

Consider U = {x|x is a positive integer greater than 1}. Which is an empty set?

{x|x ∈ U and 2x is prime}

Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. What is the probability that his model rocket has landed in a grassy area?

0.4

A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd and 154 are even. The number 8 was generated 22 times. What is the experimental probability of an even number other than 8 being generated? Write your answer as a decimal to the nearest hundredths place. The experimental probability is

0.44

The spinner is equally likely to land on any of the five sections. What is the probability that the spinner lands on an even number or on the unshaded section?

3/5

Miriam is visiting five friends in her neighborhood, Louise, Mike, Nicole, Oscar, and Pascal. In each arrangement below, the first initial of each person's name represents that person's position as he or she is visited by Miriam. Which shows all the outcomes for this event if she visits with Nicole first and Louise last?

NMOPL, NMPOL, NOPML, NOMPL, NPMOL, NPOML

Consider U = {x|x is a negative real number}. Which is an empty set?

{x|x ∈ U and x has a negative square root}

Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true?

The probability that Christina will not choose all action movies can be expressed as 1 − 9C3/20C3.

Twelve education students, in groups of four, are taking part in a student-teacher program. Mark cannot be in the first group because he will be arriving late. How many ways can the instructor choose the first group of four education students?

330

The manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots. What is the probability of a customer buying carrots?

10%

The weather report states that the probability it will rain on Wednesday is 30 percent and the probability that it will rain on Saturday is 60 percent. What is the probability that it will rain on Wednesday and on Saturday?

18 percent

Jillian has three different bracelets (X, Y, and Z) to give to her friends as gifts in any order she prefers. If bracelet Y is chosen first, in how many ways can Jillian give out the bracelets?

2

The spinner is equally likely to land on any of the six sections. What is the probability that the spinner will land on a number greater than 4 or on a shaded section?

2/3

Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag. Which shows subset A?

A = {1, 2, 3, 4, 5, 7, 8}

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference. Which choice represents the sample space, S, for this event?

S = {ABC, ABD, ACD, BCD}

Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books. If two books are randomly chosen from the collection, one at a time, and replaced after each pick, what is the probability that he first chooses an advanced book and then chooses a beginner book?

6/121

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive. What is true about spinning the spinner one time? Check all that apply.

S = {1, 2, 3, 4, 5, 6, 7, 8} If A is a subset of S, A could be {1, 2, 3}. If a subset A represents the complement of spinning an odd number, its sample space is A = {2, 4, 6, 8}.

A number cube has faces numbered 1 to 6. What is true about rolling the number cube one time? Check all that apply.

S = {1, 2, 3, 4, 5, 6} If A is a subset of S, A could be {5, 6}. If a subset A represents the complement of rolling a 5, its sample space is A = {1, 2, 3, 4, 6}.

In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red. If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

1/8

A bicycle manufacturer is studying the reliability of one of its models. The study finds that the probability of a brake defect is 4 percent and the probability of both a brake defect and a chain defect is 1 percent. If the probability of a defect with the brakes or the chain is 6 percent, what is the probability of a chain defect?

3%

A coach chooses six out of eight players to go to a skills workshop. If order does not matter, in how many ways can he choose the players for the workshop?

28

Nine wolves, eight female and one male, are to be released into the wild three at a time. If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed?

28 ways

The Venn diagram shows the number of customers who have purchased different types of pets from a pet store, where C represents customers who have purchased cats, D represents customers who have purchased dogs, and F represents customers who have purchased fish. How many people are in the set C ∩ D?

4