AnswersMath Models AProbability with Combinations and Permutations

Probability with Combinations and Permutations — Unit test Answers

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The Venn diagram shows the number of patients seen at a pediatrician’s office in one week for colds, C, ear infections, E, and allergies, A.

Question illustration
A
24
B
27
C
36
D
40
2
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Consider U = {x|x is a positive integer greater than 1}.Which is an empty set?

A
{x|x ∈ U and is prime}
Option A
B
{x|x ∈ U and 2x is prime}
C
{x|x ∈ U and can be written as a fraction}
Option C
D
{x|x ∈ U and 2x can be written as a fraction}
3

Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?

A
84
B
504
C
3,024
D
60,480
4

A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 10, 110, 60, 180. The third column is labeled Y with entries 80, 44, 59, 183. The fourth column is labeled Z with entries 61, 126, 110, 297. The fifth column is labeled Total with entries 151, 280, 229, 660.

Question illustration
A
Z and B are independent events because P(Z∣B) = P(Z).
B
Z and B are independent events because P(Z∣B) = P(B).
C
Z and B are not independent events because P(Z∣B) ≠ P(Z).
D
Z and B are not independent events because P(Z∣B) ≠ P(B).
5

Brent’s after-school game club has 12 members from which a six-member team is created. Miguel’s after-school sports club has 10 members from which a six-member team is created.Which student’s club has more possible combinations for his six-member team?

A
Brent’s club has more possible team combinations because he has fewer members on each team than Miguel’s does.
B
Brent’s club has more possible team combinations because there are more members to choose from.
C
Miguel’s club has more possible team combinations because there are fewer members in his club.
D
Miguel’s club has more possible team combinations because he has more members on each team than Brent does.
6

Will surveyed students at his school about whether they have ever gone snowboarding and whether they own a skateboard. He found that 35 of the 99 students who own a skateboard have snowboarded. Also, there were 13 students who have snowboarded but do not own a skateboard, and 147 students who have never gone snowboarding and do not own a skateboard.

A
A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 64, 99. The third column is labeled never snowboarded with entries 13, 147, 160. The fourth column is labeled Total with entries 48, 211, 256.
Option A
B
A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 13, 48. The third column is labeled never snowboarded with entries 99, 147, 246. The fourth column is labeled Total with entries 134, 160, 294.
Option B
C
A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 13, 48. The third column is labeled never snowboarded with entries 64, 147, 211. The fourth column is labeled Total with entries 99, 160, 259.
Option C
D
A 4-column table has 3 rows. The first column has entries skateboard, no skateboard, total. The second column is labeled have snowboarded with entries 35, 99, 134. The third column is labeled never snowboarded with entries 13, 147, 160. The fourth column is labeled Total with entries 48, 246, 294.
Option D
7

Four seniors and six juniors are competing for four places on a quiz bowl team.What is the approximate probability that all four seniors will be chosen at random?

A
0.00020
B
0.00476
C
0.06667
D
0.07142
8

A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the bag.What is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

A
0.02222
B
0.04444
C
0.08889
D
0.13333
9

In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

A
One-eighth
Option A
B
One-half
Option B
C
Two-thirds
Option C
D
Three-fourths
Option D
10

Which probabilities are correct? Select two options.

A
P(A|C) =
Option A
B
P(C|B) =
Option B
C
P(A) =
Option C
D
P(C) =
Option D
E
P(B|A) =
Option E
11

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.Bring lunch: 46 males, 254 femalesBuy lunch: 176 males, 264 females

A
P(buys lunch | male) = P(male) = 0.4.
B
P(male | buys lunch) = P(male) = 0.3.
C
P(buys lunch | male) = 0.3 and P(male) = 0.4.
D
P(male | buys lunch) = 0.4 and P(male) = 0.3.
12

Pedro has determined that the probability his shot will score in a lacrosse game is 0.30.What is the probability that he will score on two consecutive shots?

A
0.09
B
0.15
C
0.30
D
0.60
13

A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd and 154 are even. The number 8 was generated 22 times.What is the experimental probability of an even number other than 8 being generated? Write your answer as a decimal to the nearest hundredths place.

A
0.23
B
0.35
C
0.44
D
0.52
14

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive.What is true about spinning the spinner one time? Select three options.S = {1, 2, 3, 4, 5, 6, 7, 8}If A is a subset of S, A could be {1, 2, 3}.If A is a subset of S, A could be {7, 8, 9}.If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}.If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

A
S = {1, 2, 3, 4, 5, 6, 7, 8}
B
If A is a subset of S, A could be {1, 2, 3}.
C
If A is a subset of S, A could be {7, 8, 9}.
D
If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}.
E
If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.
15

Evaluate the expression.

Question illustration
A
3
B
6
C
60,480
D
362,874
16

Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true?

A
The probability that Christina will choose three comedies can be expressed as .
Option A
B
The probability that Christina will choose three action movies can be expressed as .
Option B
C
The probability that Christina will not choose all comedies can be expressed as 1 − .
Option C
D
The probability that Christina will not choose all action movies can be expressed as 1 − .
Option D
17

Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.Which shows subset A?

A
A = {6}
B
A = {1, 3, 5, 7}
C
A = {1, 2, 3, 4, 5, 7, 8}
D
A = {1, 2, 3, 4, 5, 6, 7, 8}
18

Which events are mutually exclusive? Select two options.

A
landing on a shaded portion and landing on an even number
B
landing on a shaded portion and landing on a number greater than 3
C
landing on a shaded portion and landing on a 3
D
landing on an unshaded portion and landing on an odd number
E
landing on an unshaded portion and landing on a number less than 2
19

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

Question illustration
A
Two-ninths
Option A
B
One-half
Option B
C
Two-thirds
Option C
D
Five-sixths
Option D
20

The cable company is analyzing the data from two satellite television providers to determine whether their users spend more time watching live television or shows that have been recorded.Satellite Company X: 89 live, 430 recordedSatellite Company Y: 65 live, 94 recorded

A
41%
B
59%
C
77%
D
83%

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