Answers LAUSD-Geometry B Prescriptive - SummerTheoretical and Experimental Probability

Unit Test Answers

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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.What is the probability of a customer buying carrots?

1.4 percent

5.0 percent

10.0 percent

11.4 percent

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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?

0.114

0.131

0.686

0.784

Information about how the students at Vista View High School got to school this morning is shown in the table.

111

114

Which statements are true? Select three options.

P(F|C) = 0.75

P(C|F) = 0.25

P(C∩F) = 0.09

P(C∩F) = P(F∩C)

P(C|F) = P(F|C)

A survey asked about the number of people who eat breakfast almost every day (B) and the number of people who buy cereal at least once a month (C). The results of the survey are shown in the Venn diagram.

StartFraction 11 Over 64 EndFraction

StartFraction 11 Over 53 EndFraction

StartFraction 53 Over 64 EndFraction

StartFraction 53 Over 57 EndFraction

There are 5 customers currently present in a coffee shop. Three of the customers are waiting in line at the front register. How many different lines of customers are possible?

120

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?

P(lotion) = 42%

P(scented) = 42%

P(shower gel | scented) = 42%

P(scented | shower gel) = 42%

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?

0.11364

0.21212

0.22727

0.42424

A survey was taken of children between the ages of 10 and 17 about how many siblings they have and whether they have a pet. The results of the survey are shown in the table.

Out of the 125 children who do not have a pet, 18 of them have 2 siblings.

Out of the 97 children who have 1 pet, 40 of them do not have any siblings.

Out of the 125 children who do not have any siblings, 34 of them have a pet.

Out of the 97 children who have 1 sibling, 40 of them do not have a pet.

The spinner is equally likely to land on any of the five sections.

Option

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?

40%

50%

60%

70%

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class.

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

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

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

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

How many 2-letter combinations can be created from the distinct letters in the word “mathematician”? Assume that the order of the letters does not matter.

156

A burrito restaurant recorded 200 customer orders. Each order was categorized by whether it was takeout or dine-in and whether it was placed on a weekday or a weekend.The results are shown below: Using this table, decide which statement about independence is true. Which statement is correct?

The events “takeout” and “weekday” are independent.

The events “weekday” and “weekend” are independent.

The events “order type” (takeout or dine-in) and “day of the week” (weekday or weekend) are not independent.

The events “takeout” and “dine-in” are independent.

three

S = {1, 2, 3, 4, 5, 6}

If A is a subset of S, A could be {0, 1, 2}.

If A is a subset of S, A could be {5, 6}.

If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}.

If a subset A represents the complement of rolling an even number, then A = {1, 3}.

A prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs.What is the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD? Express your answer in decimal form, rounded to the nearest hundredth.

0.03

0.07

0.15

0.18

Which statements are true? Select three options.

P(F|C) = 0.75

P(C|F) = 0.25

P(C∩F) = 0.09

P(C∩F) = P(F∩C)

P(C|F) = P(F|C)

Information about how the students at Vista View High School got to school this morning is shown in the table.

111

114

0.03

0.07

0.15

0.18

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}

S = {ABC, BCA, CDA, DAC}

S = {ABC, ABD, BAC, BDA, ACD, ADC, BCD, BDC}

S = {ABC, ABD, ACD, BCA, BCD, BDC, CAB, CBD, DAC, DBC}

Option

Hana has a bag containing one red (R), one blue (B), and one yellow (Y) tile. She draws two tiles out of the bag, one after the other. Which explanation and tree diagram represent a pair of dependent of events?

Once a tile is chosen, it can be chosen again:

Once a tile is chosen, it cannot be chosen again:

Once a tile is chosen, it can be chosen again:

There are 22 participants in a spelling bee. In how many ways can the top 5 participants finish? Use the formula for permutations to find your answer.

26,334

632,016

3,160,080

5,153,632

Which best describes independent events?

The results of all events have different individual probabilities.

The results of any previous events affects the probability of future events.

The results of all events have the same individual probability.

The results of all previous events do not affect the probability of future events.

A survey was taken of children between the ages of 10 and 17 about how many siblings they have and whether they have a pet. The results of the survey are shown in the table.

Out of the 125 children who do not have a pet, 18 of them have 2 siblings.

Out of the 97 children who have 1 pet, 40 of them do not have any siblings.

Out of the 125 children who do not have any siblings, 34 of them have a pet.

Out of the 97 children who have 1 sibling, 40 of them do not have a pet.

A 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?

0.00595

0.03571

0.11111

0.66667

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class.

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

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

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

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

Events X and Y are independent. The probability of X occurring is . The probability of Y occurring is . What is P(X and Y)?

Option

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?

2 percent

18 percent

60 percent

90 percent

The events “takeout” and “weekday” are independent.

The events “weekday” and “weekend” are independent.

The events “order type” (takeout or dine-in) and “day of the week” (weekday or weekend) are not independent.

The events “takeout” and “dine-in” are independent.

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