AnswersConcepts in Probability and Statistics AProperties of Probability Distributions

Properties of Probability Distributions — Unit test Answers

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

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11
7
74
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111
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114
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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?

A
StartFraction 30 P 2 Over 50 P 2 EndFraction
Option A
B
StartFraction 30 C 2 Over 50 C 2 EndFraction
Option B
C
StartFraction (10 C 1) (20 C 1) Over 50 C 2 EndFraction
Option C
D
StartFraction (10 P 1) (20 P 1) Over 50 P 2 EndFraction
Option D
3

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?

A
P(lotion) = 42%
B
P(scented) = 42%
C
P(shower gel | scented) = 42%
D
P(scented | shower gel) = 42%
4

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?

A
0.00595
B
0.03571
C
0.11111
D
0.66667
5

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
1.4 percent
B
5.0 percent
C
10.0 percent
D
11.4 percent
6

Which statements are true? Select three options.

A
P(F|C) = 0.75
B
P(C|F) = 0.25
C
P(C∩F) = 0.09
D
P(C∩F) = P(F∩C)
E
P(C|F) = P(F|C)
7

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

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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.

A
0.03
B
0.07
C
0.15
D
0.18
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 S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

A
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.43; 1 time is 0.43; 2 times is 0.1.
Option A
B
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.33; 1 time is 0.33; 2 times is 0.33.
Option B
C
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.55; 1 time is 0.32; 2 times is 0.11.
Option C
D
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.5; 1 time is 0.38; 2 times is 0.12.
Option D
10

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?

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Which best describes independent events?

A
The results of all events have different individual probabilities.
B
The results of any previous events affects the probability of future events.
C
The results of all events have the same individual probability.
D
The results of all previous events do not affect the probability of future events.
12

Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white.

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A
0.2
B
0.3
C
0.4
D
0.6
13

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?

A
2 percent
B
18 percent
C
60 percent
D
90 percent
14

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
B
0.131
C
0.686
D
0.784
15

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

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