AnswersConcepts in Probability and StatisticsApplications of Probability

Practice Test Answers

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Given that a randomly chosen person eats breakfast almost every day, what is the probability that the person also buys cereal at least once a month?

A
53 over 57
B
53 over 64
C
11 over 64
D
11 over 53
4
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A number cube has faces numbered 1 to 6 What is true about rolling the number cube one time? Choose three correct answers.

A
cap s is equal to 1 comma 2 comma 3 comma 4 comma 5 comma 6
B
If a subset cap A represents the complement of rolling a 5 , then cap A is equal to 1 comma 2 comma 3 comma 4 comma 6 .
C
If cap A is a subset of cap s , cap A could be start set 0 comma 1 comma 2 end set .
D
If a subset cap A represents the complement of rolling an even number, then cap A is equal to 1 comma 3 .
E
If cap A is a subset of cap s , cap A could be start set 5 comma 6 end set .
5

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?

A
86 point 7 percent
B
13 point 3 percent
C
84 point 6 percent
D
15 point 4 percent
6

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?

A
1 point 4 percent
B
11 point 4 percent
C
10 point 0 percent
D
5 point 0 percent
7

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?

A
40 percent
B
70 percent
C
60 percent
D
50 percent
8

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?

A
5 over 11
B
6 over 121
C
5 over 121
D
6 over 11
9

Veronique has a spinner with three sections of equal size, red r , green g , and blue b The spinner is spun twice. The sample space for the possible outcomes is cap s is equal to rr, rb, rg, gr, gg, gb, br, bg, bb If the number of times red is spun is the random variable, cap x , which graph represents the probability distribution?

A
Image with description Bar graph titled “Probability Distribution.” The horizontal axis, labeled X, shows the outcomes “0 times,” “1 time,” and “2 times.” The vertical axis, labeled P subscript X of x, ranges from 0 to 0.6 with tick marks at intervals of 0.1. Three bars are displayed. The bar for “0 times” has height 0.5, the bar for “1 time” has height approximately 0.35, and the bar for “2 times” has height approximately 0.15. The graph shows that the probability decreases as the number of occurrences increases.
B
Image with description Bar graph titled “Probability Distribution.” The horizontal axis, labeled X, shows three outcomes: “0 times,” “1 time,” and “2 times.” The vertical axis, labeled Pₓ(x), ranges from 0 to 0.4 with tick marks at 0.1 intervals. Three bars are shown, one above each outcome, and all three bars have the same height, approximately 0.33 (one-third). This indicates that the probabilities of X being 0, 1, or 2 are equal.
C
Image with description The bar graph entitled Probability Distribution represents the probability of how many times the color red is spun as a random variable. The x axis shows the possible values of the variable X, from 0 times to 1 time and 2 times, while the y axis shows the probability ranging from 0 to 0 point 6, in increments of 0.1, labeled as P subscript x of x. There are 3 bars. The first bar is at 0 times and its height is 0 point 55, the second bar is at 1 time and its height is 0 point 32, and the third bar is at 2 times and its height is 0 point 11.
D
Image with description Bar graph titled “Probability Distribution.” The horizontal axis, labeled X, shows three outcomes: “0 times,” “1 time,” and “2 times.” The vertical axis, labeled Pₓ(x), ranges from 0 to 0.4 with tick marks at 0.1 intervals. Three bars are shown, one above each outcome, and all three bars have the same height, approximately 0.33 (one-third). This indicates that the probabilities of X being 0, 1, or 2 are equal.
10

The number of absences for one week for all students at a high school were compiled, and the probability distribution was created. What is the probability in any given week that a randomly selected student will be absent no more than one day? Probability Distribution Days Absent: cap x Probability: cap p times cap x 0 0 point 7 8 1 0 point 1 4 2 0 point 0 3 3 0 point 0 1 4 0 5 0 point 0 4

A
0 point 7 8
B
0 point 0 8
C
0 point 9 2
D
0 point 1 4
11

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?

A
Once a tile is chosen, it can be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into B and Y. From B, the second level branches into R and Y. From Y, the second level branches into R and B. Each second-level branch excludes the tile already drawn at the first level.
B
Once a tile is chosen, it cannot be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into B and Y. From B, the second level branches into R and Y. From Y, the second level branches into R and B. Each second-level branch excludes the tile already drawn at the first level.
C
Once a tile is chosen, it cannot be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into R, B and Y. From B, the second level branches into R, B and Y. From Y, the second level branches into R, B and Y.
D
Once a tile is chosen, it can be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into R, B and Y. From B, the second level branches into R, B and Y. From Y, the second level branches into R, B and Y.
12

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?

A
the fraction with numerator open paren sub 10 cap c sub 1 close paren times open paren sub 20 cap c sub 1 close paren and denominator sub 50 cap c sub 2
B
the fraction with numerator sub 30 cap c sub 2 and denominator sub 50 cap c sub 2
C
the fraction with numerator open paren sub 10 cap p sub 1 close paren times open paren sub 20 cap p sub 1 close paren and denominator sub 50 cap p sub 2
D
the fraction with numerator sub 30 cap p sub 2 and denominator sub 50 cap p sub 2
13

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 percent 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?

A
cap p times lotion is equal to 42 percent
B
cap p times scented is equal to 42 percent
C
cap p times open paren scented divides shower gel close paren is equal to 42 percent
D
cap p times open paren shower gel divides scented close paren is equal to 42 percent
14

Events X and Y are independent. The probability of X occurring is 1 third The probability of Y occurring is 1 half What is cap p times open paren cap x And cap y close paren ?

A
2 thirds
B
5 sixths
C
1 sixth
D
1 third

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