AnswersAlgebra 2 with ProbabilityProbability Rules

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Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The favorite café of the person associated with the selected marble is chosen for that week’s meeting. Which of the following represents the sample space for choosing a café for the first two weeks?

A
R & G, R & B, G & R, G & B, B & R, B & G
B
R & R, R & G, R & B, R & G, G & R, G & G, G & B, B & R, B & G, B & B
C
R & R, R & G, R & B, G & R, G & G, G & B, B & R, B & G, B & B
D
R & R, R & G, R & B, G & G, G & B, B & B
2
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A group of ticket takers at a box office for a new theater noticed that in the first year of the theater’s operation, the genre breakdown of the movies was 10 percent horror, 39 percent comedy, 28 percent drama, and 23 percent action. If a movie from the theater’s first year of operation was selected at random, which of the following identifies the probability distribution for the movie’s genre?

A
Table with 4 columns and 2 rows.Row 1: Column 1, 'Action'; Column 2, 'Comedy'; Column 3, 'Drama'; Column 4, 'Horror' Row 2: Column 1, '0 point 3 9'; Column 2, '0 point 2 3'; Column 3, '0 point 1 0'; Column 4, '0 point 2 8'
B
Table with 4 columns and 2 rows.Row 1: Column 1, 'Action'; Column 2, 'Comedy'; Column 3, 'Drama'; Column 4, 'Horror' Row 2: Column 1, '0 point 2 3'; Column 2, '0 point 3 9'; Column 3, '0 point 2 8'; Column 4, '0 point 1 0'
C
Table with 4 columns and 2 rows.Row 1: Column 1, 'Action'; Column 2, 'Comedy'; Column 3, 'Drama'; Column 4, 'Horror' Row 2: Column 1, '0 point 3 9'; Column 2, '0 point 1 0'; Column 3, '0 point 2 3'; Column 4, '0 point 2 8'
D
Table with 4 columns and 2 rows.Row 1: Column 1, 'Action'; Column 2, 'Comedy'; Column 3, 'Drama'; Column 4, 'Horror' Row 2: Column 1, '0 point 1 0'; Column 2, '0 point 3 9'; Column 3, '0 point 2 8'; Column 4, '0 point 2 3'
3

A popular board game has players twist their bodies around so that their hands and feet touch small colored dots. A spinner with equal areas for each body part (left hand, right hand, left foot, or right foot) is used. Which of the following is the correct probability distribution for the body part chosen to be placed?

A
Table with 4 columns and 2 rows.Row 1: Column 1, 'LH'; Column 2, 'RH'; Column 3, 'LF'; Column 4, 'RF' Row 2: Column 1, '0 point 2 5'; Column 2, '0 point 2 5'; Column 3, '0 point 2 5'; Column 4, '0 point 2 5'
B
Table with 4 columns and 2 rows.Row 1: Column 1, 'LH'; Column 2, 'RH'; Column 3, 'LF'; Column 4, 'RF' Row 2: Column 1, '4'; Column 2, '4'; Column 3, '4'; Column 4, '4'
C
Table with 4 columns and 2 rows.Row 1: Column 1, 'LH'; Column 2, 'RH'; Column 3, 'LF'; Column 4, 'RF' Row 2: Column 1, '1'; Column 2, '1'; Column 3, '1'; Column 4, '1'
D
Table with 4 columns and 2 rows.Row 1: Column 1, 'LH'; Column 2, 'RH'; Column 3, 'LF'; Column 4, 'RF' Row 2: Column 1, '0 point 5 0'; Column 2, '0 point 2 5'; Column 3, '0 point 5 0'; Column 4, 'negative 0 point 2 5'
4

Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The favorite café of the person associated with the selected marble is chosen for that week’s meeting. What is the probability that Reese will get to pick the café for at least one of the first two weeks?

A
5 ninths
B
1 third
C
1 half
D
2 thirds
5

Some college advisors noticed the following breakdown of majors for the incoming freshman at their school: 3 percent math, 22 percent nursing, 16 percent psychology, 11 percent criminal justice, and 48 percent business. Suppose a first-year student was chosen at random. Which of the following is the probability distribution for that student’s major?

A
Table with 5 columns and 2 rows.Row 1: Column 1, 'Business'; Column 2, 'Criminal Justice'; Column 3, 'Math'; Column 4, 'Nursing'; Column 5, 'Psychology' Row 2: Column 1, '0 point 0 3'; Column 2, '0 point 1 1'; Column 3, '0 point 4 8'; Column 4, '0 point 2 2'; Column 5, '0 point 1 6'
B
Table with 5 columns and 2 rows.Row 1: Column 1, 'Business'; Column 2, 'Criminal Justice'; Column 3, 'Math'; Column 4, 'Nursing'; Column 5, 'Psychology' Row 2: Column 1, '0 point 2 2'; Column 2, '0 point 0 3'; Column 3, '0 point 1 6'; Column 4, '0 point 4 8'; Column 5, '0 point 1 1'
C
Table with 5 columns and 2 rows.Row 1: Column 1, 'Business'; Column 2, 'Criminal Justice'; Column 3, 'Math'; Column 4, 'Nursing'; Column 5, 'Psychology' Row 2: Column 1, '0 point 4 8'; Column 2, '0 point 1 1'; Column 3, '0 point 0 3'; Column 4, '0 point 2 2'; Column 5, '0 point 1 6'
D
Table with 5 columns and 2 rows.Row 1: Column 1, 'Business'; Column 2, 'Criminal Justice'; Column 3, 'Math'; Column 4, 'Nursing'; Column 5, 'Psychology' Row 2: Column 1, '0 point 4 8'; Column 2, '0 point 1 1'; Column 3, '0 point 3 0'; Column 4, '0 point 2 2'; Column 5, '0 point 1 6'
6

Three siblings, Peyton, Cameron, and Dakota, all ask their parents to borrow the family car for different events around town. Since they cannot all borrow the car at the same time, the parents decide to use randomness to decide who gets the car. They will roll a single, fair, six-sided number cube. Peyton gets the car if a 1 or 2 is rolled. Cameron gets the car if a 3 or 4 is rolled, and Dakota gets the car if a 5 or 6 is rolled. Which of the following is the probability distribution for who gets the car?

A
Table with 3 columns and 2 rows.Row 1: Column 1, 'Peyton'; Column 2, 'Cameron'; Column 3, 'Dakota' Row 2: Column 1, '0 point 3'; Column 2, '0 point 3'; Column 3, '0 point 3'
B
Table with 3 columns and 2 rows.Row 1: Column 1, 'Peyton'; Column 2, 'Cameron'; Column 3, 'Dakota' Row 2: Column 1, '1 third'; Column 2, '1 third'; Column 3, '1 third'
C
Table with 3 columns and 2 rows.Row 1: Column 1, 'Peyton'; Column 2, 'Cameron'; Column 3, 'Dakota' Row 2: Column 1, '1 sixth'; Column 2, '1 sixth'; Column 3, '1 sixth'
D
Table with 3 columns and 2 rows.Row 1: Column 1, 'Peyton'; Column 2, 'Cameron'; Column 3, 'Dakota' Row 2: Column 1, '1'; Column 2, '1'; Column 3, '1'
7

A movie enthusiast is going to select 1 of 4 movies (labeled W, X, Y, and Z) using a random method where all the movies are equally likely to be chosen. Which of the following is the probability distribution for the movie selection?

A
Table with 4 columns and 2 rows.Row 1: Column 1, 'W'; Column 2, 'X'; Column 3, 'Y'; Column 4, 'Z' Row 2: Column 1, '0 point 4 0'; Column 2, '0 point 4 0'; Column 3, '0 point 4 0'; Column 4, '0 point 4 0'
B
Table with 4 columns and 2 rows.Row 1: Column 1, 'W'; Column 2, 'X'; Column 3, 'Y'; Column 4, 'Z' Row 2: Column 1, '0 point 1 0'; Column 2, '0 point 2 0'; Column 3, '0 point 3 0'; Column 4, '0 point 4 0'
C
Table with 4 columns and 2 rows.Row 1: Column 1, 'W'; Column 2, 'X'; Column 3, 'Y'; Column 4, 'Z' Row 2: Column 1, '0 point 2 5'; Column 2, '0 point 2 5'; Column 3, '0 point 2 5'; Column 4, '0 point 2 5'
D
Table with 4 columns and 2 rows.Row 1: Column 1, 'W'; Column 2, 'X'; Column 3, 'Y'; Column 4, 'Z' Row 2: Column 1, '0 point 5 0'; Column 2, '0 point 5 0'; Column 3, '0 point 5 0'; Column 4, 'negative 0 point 5 0'
8

A group of dental researchers are testing the effects of acidic drinks on dental crowns. They have five containers of crowns labeled V, W, X, Y, and Z. They will randomly select one of the containers to be the control for the experiment by drawing one of five well-mixed slips of paper with the same labels from a hat. Which of the following is the probability model for the control container?

A
Table with 5 columns and 2 rows.Row 1: Column 1, 'V'; Column 2, 'W'; Column 3, 'X'; Column 4, 'Y'; Column 5, 'Z' Row 2: Column 1, '5'; Column 2, '5'; Column 3, '5'; Column 4, '5'; Column 5, '5'
B
Table with 5 columns and 2 rows.Row 1: Column 1, 'V'; Column 2, 'W'; Column 3, 'X'; Column 4, 'Y'; Column 5, 'Z' Row 2: Column 1, '0 point 2 0'; Column 2, '0 point 1 0'; Column 3, '0 point 3 0'; Column 4, '0 point 2 0'; Column 5, '0 point 2 0'
C
Table with 5 columns and 2 rows.Row 1: Column 1, 'V'; Column 2, 'W'; Column 3, 'X'; Column 4, 'Y'; Column 5, 'Z' Row 2: Column 1, '0 point 2 5'; Column 2, '0 point 2 5'; Column 3, '0 point 2 5'; Column 4, '0 point 2 5'; Column 5, '0 point 2 5'
D
Table with 5 columns and 2 rows.Row 1: Column 1, 'V'; Column 2, 'W'; Column 3, 'X'; Column 4, 'Y'; Column 5, 'Z' Row 2: Column 1, '0 point 2 0'; Column 2, '0 point 2 0'; Column 3, '0 point 2 0'; Column 4, '0 point 2 0'; Column 5, '0 point 2 0'
9

A group of marketing researchers for a popular cell phone manufacturer collected the following information about young adults (aged 18 – 25 ): 1 percent use a cell phone that is 3 years or older, 2 percent use a cell phone that is 2 – 3 years old, 20 percent use a cell phone that is 1 – 2 years old, and 77 percent use a cell phone that is less than 1 year old. Suppose a young adult was selected at random. Let cap x equal the age of a randomly selected person’s cell phone. Which of the following is the probability distribution for the age of that person’s cell phone?

A
Table with 4 columns and 2 rows.Row 1: Column 1, '<1'; Column 2, '1≤X<2'; Column 3, '2≤X<3'; Column 4, 'is greater than or equal to 3' Row 2: Column 1, '0 point 7 7'; Column 2, '0 point 2 0'; Column 3, '0 point 2'; Column 4, '0 point 1'
B
Table with 4 columns and 2 rows.Row 1: Column 1, '<1'; Column 2, '1≤X<2'; Column 3, '2≤X<3'; Column 4, 'is greater than or equal to 3' Row 2: Column 1, '0 point 7 7'; Column 2, '0 point 2 0'; Column 3, '0 point 0 2'; Column 4, '0 point 0 1'
C
Table with 4 columns and 2 rows.Row 1: Column 1, '<1'; Column 2, '1≤X<2'; Column 3, '2≤X<3'; Column 4, 'is greater than or equal to 3' Row 2: Column 1, '0 point 2 5'; Column 2, '0 point 2 5'; Column 3, '0 point 2 5'; Column 4, '0 point 2 5'
D
Table with 4 columns and 2 rows.Row 1: Column 1, '<1'; Column 2, '1≤X<2'; Column 3, '2≤X<3'; Column 4, 'is greater than or equal to 3' Row 2: Column 1, '0 point 0 1'; Column 2, '0 point 0 2'; Column 3, '0 point 2 0'; Column 4, '0 point 7 7'
10

A six-sided number cube is considered "loaded” if it is not fair. Which of the following could be the probability distribution for a loaded number cube?

A
Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '0 point 2 0'; Column 2, '0 point 1 5'; Column 3, '0 point 2 0'; Column 4, '0 point 2 0'; Column 5, '0 point 2 0'; Column 6, '0 point 2 0'
B
Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '0 point 0 5'; Column 2, '0 point 1 2'; Column 3, '0 point 2 3'; Column 4, '0 point 1 0'; Column 5, '0 point 2 4'; Column 6, '0 point 2 6'
C
Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '1 sixth'; Column 2, '1 sixth'; Column 3, '1 sixth'; Column 4, '1 sixth'; Column 5, '1 sixth'; Column 6, '1 sixth'
D
Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '0 point 2 0'; Column 2, 'negative 0 point 1 0'; Column 3, '0 point 2 5'; Column 4, '0 point 1 5'; Column 5, '0 point 3 0'; Column 6, '0 point 2 0'

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