Notes

S is a subset within a universal set, U.

If S = {x, y, 4, 9, ?), which could describe U?

A: U = {keys on a keyboard}
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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 x + 3 ≤ 4}

For which values of x is A ⋃ B = Ø?

A: 2 < x < 3
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Consider U = {x|x is a real number}.

A = {x|x ∈ U and x + 2 > 10}
B = {x|x ∈ U and 2x > 10}

Which statements are true?

C: 8 ∉ A; 8 ∈ B
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On the Venn diagram, which region(s) represent the intersection of Set A and Set B (A∩B)?

A: II
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Consider U = {x|x is a negative real number}.

Which is an empty set?

B: {x|x ∈ U and x has a negative square root}
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How many of the parallelograms fall into the category AUB?

A: 26
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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?

B: positive numbers
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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?

C: 62/95
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A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.

What is the theoretical probability that applesauce and broccoli will both be offered on Monday?

B: 20%
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Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order.

What is the sample space showing the possible orders of the other three runners?

C: S = {FGI, FIG, GFI, GIF, IFG, IGF}
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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?

B: choosing five CDs where not all of them are pop
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A random number generator is used to create a list of 150 single-digit numbers. Of those 150 numbers, 72 are odd and 78 are even. The number 9 was generated 15 times.

To the nearest whole percent, what is the experimental probability of an odd number other than 9 being generated?

A: 38%
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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?

D: 4,920 out of 5,040
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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?

D: S = {PQ, QP, PR, RP, QR, RQ}
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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?

D: 31%
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Dayshawn can choose two of his four t-shirts to take on a weekend trip.

If the t-shirts are labeled A, B, C, and D, which choice represents the sample space, S, for the event?

C: S = {AB, AC, AD, BC, BD, CD}
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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?

C: 20 percent
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What is the probability that a person chosen at random from this group has brown or green eyes?
13/25
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What is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?

D: 6/11
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The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1.

The events are not independent because the

Product of P (A) and P (B) is not equal to P(A and B)
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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?

C: P(largest or smallest) = 0.30 + 0.20 - 0.15
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Two surveys are chosen at random from the group of surveys. After the first survey is chosen, it is returned to the stack and can be chosen a second time. What is the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family?

1/50
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Which events are independent? Check all that apply.

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

C: 5/136
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To the nearest whole percent, what is the probability that when she opens a random picture from the computer folder, it will be a blurry picture she took with her cell phone?

A:7%
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What is the probability that both of Eduardo’s partners for the group project will be girls?

B: 24/65
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Twenty-two percent of the large pieces of mail that Rachel received this week were magazines and the rest were catalogs. Of the catalogs, 36 percent were for clothing.

To the nearest whole percent, what is the probability that a randomly chosen large piece of Rachel’s mail was a clothing catalog?

B:28%
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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.

.13
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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?

A: 13%
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If events A and B are independent, and the probability that event A occurs is 83%, what must be true?

C: The probability that event A occurs, given that event B occurs, is 83%.
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in the drawing, six out of every 10 tickets are winning tickets. Of the winning tickets, one out of every three awards is a larger prize.

What is the probability that a ticket that is randomly chosen will award a larger prize?

B: 1/5
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Which statement is true about whether C and Y are independent events?

D: C and Y are not independent events because P(C∣Y) ≠ P(C).
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A survey was taken of children between the ages of 7 and 12. Let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings.

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

D: A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.
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The two-way table shows the number of books of each type in Eliza’s home.

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

B: 0.4
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Which two events are independent?

A: A and X
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Which statements are true? Check all that apply.

1: Milk was requested for 16 of the large-sized meal orders.
4: Sixty-three of the orders of soda came with a regular-sized meal.
5: A total of 124 large-sized meals were ordered.
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Information about the students at Jackson High School is shown in the table.

Which statement must be true?

A: Out of the 352 eleventh graders at the school, 173 of them are girls.
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The two-way table shows the estimated number of students who will enroll in three area high schools next year.

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

.4
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The two-way table shows the preferred vacation destination for people in different age groups.

Which statement is true?

D: The probability that a randomly selected person who chose Mexico as the preferred destination is a child is 14/113
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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?

D: 0.1275
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Two unique letters are chosen at random from the alphabet.

What is the approximate probability that the first letter chosen is A?

A: 0.0385
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Six girls and four boys have entered the science fair. First, second, and third place awards are to be given out.

What is the probability that exactly one girl and two boys will receive awards? Express your answer as a percent.

10%
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Four girls and six boys are in a Spanish club. Three of the people will be chosen at random to represent the group in a photograph.

What is the probability that one girl and two boys will be chosen?

50%
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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?

C: (3C1)(4C1)/12C2
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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?

C: 36%
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Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.

What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.

30%
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A lock is opened using a sequence of three numbers. The numbers range from 0 to 39, inclusive, and cannot be repeated within the sequence.

What is the probability that all the numbers in the sequence are even? Express your answer as a percent and round to the nearest whole number.

12%
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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?

D: (4C1)(4C1)/52C2
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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?

A: 12P3/22P3
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At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.

What is the approximate probability that a student chooses a computer elective and an art elective?

C: 0.22727
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A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the bag.

Which expression represents the probability that one of the marbles is red and the other is blue?

C: (10C1)(20C1)/50C2
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A librarian has 10 nonfiction and eight fiction books from which to choose the next three book club selections.

What is the approximate probability that she chooses a fiction book, then a nonfiction book, then a fiction book?

A: 0.114
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What is the probability that his model rocket has landed in a grassy area?

C: 0.4
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Which statement is true about whether A and B are independent events?

A: A and B are independent events because P(A∣B) = P(A).
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Which is a subset of I?

A: E
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Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel.

For the events "shower gel” and "scented” to be independent, what must be shown to be true?

C: P(shower gel | scented) = 42%
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What is the probability that the spinner lands on an even number or on the unshaded section?

C: 3/5
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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?

B: 18 percent
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Given that a randomly chosen person eats breakfast almost everyday, what is the probability that the person also buys cereal at least once a month?

C: 53/64
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Which statements are true? Check all that apply.

1: P(F|C) = 0.75
3: P(C∩F) = 0.09
4: P(C∩F) = P(F∩C)
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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?

B: 6/121
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three-digit personal identification number is chosen using the digits 1–9. The digits cannot be repeated.

What is the approximate probability that the first digit will be 6?

C: 0.11111
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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.

10%
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