UNIT: APPLICATIONS OF PROBABILITY

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

B ⊂ A

To the nearest tenth, what is the value of P(Y|B)?

.4

On the Venn diagram, which region(s) represent the union of Set A and Set B (A⋃B)?

NOT - I and III YES - II

The events "male" and "buys lunch" are not independent because

P(male | buys lunch) = 0.4 and P(male) = 0.3.

A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random. What is the approximate probability of choosing one club and one heart?

0.1275

Seventy-five percent of the flowers in the arrangement are roses and the rest are tulips. Of the tulips, 50 percent are pink. To the nearest whole percent, what is the probability that a randomly chosen flower from the arrangement is a pink tulip?

13%

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

Which statement is true about whether A and B are independent events?

A and B are independent events because P(A∣B) = P(A) = 0.16.

The track team gives awards for first, second, and third place runners. There are 10 students from school A and 12 students from school B competing. Which expression represents the probability that all three awards will go to a student from school B?

NOT - 13C3/22C3

Which probability is correct?

NOT - P(B|A) = 7/20

A six-sided number cube is rolled twice. What is the probability that the first roll is an even number and the second roll is a number greater than 4?

1/6

What is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?

6/11

In a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. Each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10. If event A is choosing a king, event B is choosing a heart, and event C is choosing a jack, which Venn diagram could represent this description?

A

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}

A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs. To the nearest whole percent, what is the probability that a car is an SUV, given that it is white?

NOT - 57% YES - 15%

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?

NOT - 80 percent

Which probability is correct?

P(A) = 3/5

Which events are mutually exclusive? Select two options.

landing on a shaded portion and landing on a number greater than 3 landing on an unshaded portion and landing on an odd number

Carrie is finding the set of even numbers within the set of prime numbers. Of the sets described, which is the universal set?

prime numbers

To the nearest whole percent, what is the probability that a randomly selected customer from Satellite Company Y watches recorded shows more often than live television?

59%

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag. What is the approximate probability that exactly two of the five are blue?

36%

How many people are in the set C ∩ D?

4

For the soccer banquet, the players and their family members selected their favorite main dish and side dish. Of the 39 people who chose chicken as the main dish, 18 wanted potatoes. Of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. A total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish. Which two-way table correctly displays this data?

B

Lola pulls two marbles from a bag containing four red marbles, four blue marbles, and 12 yellow marbles without replacing them. What is the probability that she pulled out a red marble first and a yellow marble second? Express your answer in decimal form, rounded to the nearest hundredth.

0.13

A hat contains slips of paper with the names of the 26 other students in Eduardo's class on them, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them. What is the probability that both of Eduardo's partners for the group project will not be boys?

24/65

A landscaper is selecting two trees to plant. He has five to choose from. Three of the five are deciduous and two are evergreen. What is the probability that he chooses trees of two different types? Express your answer as a percent.

60%

A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver's licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver's licenses and take the bus to school every day. To the nearest whole percent, what is the probability that a senior takes the bus to school every day, given that he or she has a driver's license?

17%

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president. Which choice represents the sample space, S, for this event?

S = {PQ, QP, PR, RP, QR, RQ}

Four seniors and six juniors are competing for four places on a quiz bowl team. What is the approximate probability that all four seniors will be chosen at random?

0.00476

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

How many framed prints did Mr. Carandang sell?

517

What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings? Round to the nearest whole percent.

70%

Information about the recycling drive at school is shown in the table. Let A be the event that the item pulled out of the recycling bin is a plastic bottle, and let B be the event that a tenth grader recycled that item. Which statement is true about whether A and B are independent events?

A and B are not independent events because P(A∣B) ≠ P(A).

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the probability that both students chosen are sophomores?

NOT - (6P1)(5P1)/20P2

Which statement must be true?

Out of the 352 eleventh graders at the school, 173 of them are girls.

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.

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}

To the nearest tenth, what is the value of P(C|Y)?

0.5

Which number(s) satisfy A ∩ C?

NOT - 16, 81 YES - 1, 16, 81

Consider the following sets. U = {ordered pairs on a coordinate plane}A = {ordered pair solutions to y = x}B = {ordered pair solutions to y = 2x} Which ordered pair satisfies A ∩ B?

(0, 0)

A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the bag. What is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

0.04444

What is the probability that a randomly selected reference book is hardcover?

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.

0.44

How many students chose to participate in the painting class?

17

The Hawaiian language has 12 letters: five vowels and seven consonants. Each of the 12 Hawaiian letters are written on a slip of paper and placed in the bag. A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag. What is the probability that two vowels are chosen?

25/144

A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0-9. Each character in the password cannot be used more than once. What is the approximate probability that exactly one of the four characters will be a number?

28%

Of all of the medium mirrors that were shipped, how many of them were broken?

NOT - 78 YES - 68

Which statements are true about Yuri's experiment? Select three options.

The theoretical probability of spinning any one of the five colors is 20%. The theoretical probability of spinning green is equal to the experimental probability of spinning green. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Which statement is true about whether Z and B are independent events?

Z and B are independent events because P(Z∣B) = P(Z).

A restaurant offers three vegetable side dishes, two fruit side dishes, and five grain-based side dishes. Each entree comes with two side dishes. What is the approximate probability of randomly choosing one vegetable and one grain-based side dish?

0.33333

Two children are playing a code-breaking game. One child makes a sequence of three colors from red, yellow, blue, and purple. The other child must guess the sequence of colors in the correct order. Once one color is used, it cannot be repeated in the sequence. What is the probability that the sequence is guessed on the first try?

1/24

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

What is the probability that a person chosen at random from this group has brown or green eyes?

13/25

Izzy randomly throws a dart at the square, and it lands inside the square. To the nearest percent, what is the probability that the dart lands inside the square but not on the circular dartboard? Use 3.14 for π.

22%

How many patients had allergies or ear infections, but not both?

24

A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters. A dart is randomly thrown at the board. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle? Round to the nearest whole percent.

25%

Given that a randomly chosen quadrilateral has four right angles, what is the probability that the quadrilateral also has four equal side lengths? Express your answer in percent form, rounded to the nearest whole percent.

25%

Jasmine rolls a number cube 72 times. The number 2 is rolled 13 times and the number 3 is rolled nine times. To the nearest whole percent, what is the experimental probability of rolling a 2 or 3?

31%

Which two events are independent?

A and X

Consider the following sets. U = {all real number points on a number line}A = {solutions to the inequality 3x + 4 ≥ 13}B = {solutions to the inequality 1/2x + 3 ≤ 4} For which values of x is A ⋃ B = Ø?

NOT - 2 ≤ x ≤ 3 NOT - x ≤ 2 and x ≥ 3

If events A and B are independent, what must be true?

P(A|B) = P(A)

If events A and B are independent, and the probability that event A occurs is 83%, what must be true?

The probability that event A occurs, given that event B occurs, is 83%.

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive. What is true about spinning the spinner one time? Select three options.

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, then A = {2, 4, 6, 8}.

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives. Which expression represents the probability that a student chooses an art elective and a history elective?

(3C1)(4C1)/12C2

A standard deck of 52 playing cards contains four of each numbered card 2-10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random. Which expression represents the probability of drawing a king and a queen?

(4C1)(4C1)/52C2

What is the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number?

24/121

When a softball player gets a hit, it can be a single, double, triple, or home run. When Josephine is at bat, the probability that she hits a single is 15 percent and the probability that she hits a double is 5 percent. What is the probability that Josephine hits a single or a double when she is at bat?

20 percent

If U = {all positive integers} and A = {x|x ∈ U and x is an odd positive integer}, which describes Ac?Ac = {x|x ∈ U and is an even positive integer}

Ac = {x|x ∈ U and is an even positive integer}

Which two-way table correctly displays this data?

C

Two unique letters are chosen at random from the alphabet. What is the approximate probability that the first letter chosen is A?

NOT - 0.0800

In decimal form, to the nearest tenth, what is the probability that a randomly selected Riverside High School student is in twelfth grade?

NOT - 0.5

What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?

NOT - 0.6

The Venn diagram shows three types of numbers: odd (O), even (E), and prime (P). Which is represented by Ø?

NOT - O ⋃ E YES - E ∩ O

The universal set is the set of rational numbers. S is the set of integers. Which represents Sc?

NOT - {x|x is a rational positive number} NOT.- {x|x is a real number}

Which probabilities are correct? Select two options.

P(A|C) =2/3 P(A) =31/59

An amusement park reports that the probability of a visitor riding its largest roller coaster is 30 percent, the probability of a visitor riding its smallest roller coaster is 20 percent, and the probability of a visitor riding both roller coasters is 15 percent. Which equation can be used to calculate the probability of a visitor riding the largest or the smallest roller coaster?

P(largest or smallest) = 0.30 + 0.20 - 0.15

Which scenario depicts two independent events?

The school play opens tonight and it is raining.

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

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

A security alarm requires a four-digit code. The code can use the digits 0-9 and the digits cannot be repeated. Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7?

(10P1)(9P3)/10P4

What is the probability that the spinner will land on a number greater than 4 or on a shaded section?

2/3

A padlock has a four-digit code that includes digits from 0 to 9, inclusive. What is the probability that the code does not consist of all odd digits if the same digit is not used more than once in the code?

4,920 out of 5,040

Nadia's bookshelf contains 10 fiction books, two reference books, and five nonfiction books. What is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book?

5/136

Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking. What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?

A = {KL}

April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs. What is the complement of April choosing five pop CDs?

choosing five CDs where not all of them are pop