AnswersConcepts in Probability and Statistics AUnit Test

Unit Test — Unit test Answers

25 verified answers
1
Free Preview

A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.What is the approximate probability that exactly one of the four characters will be a number?

A
1%
B
11%
C
28%
D
44%
2
Free Preview

best

t
two or more events that have the same probabilities.
t
two or more events that do not have the same probabilities.
a
a group of events whose later outcomes are not affected by previous outcomes.
a
a group of events whose later outcomes are affected by previous outcomes.
3

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
4

Luka has a bag containing 5 socks: 3 red, 1 white, and 1 black. He draws 1 sock out of the bag, replaces it, and then draws another sock.What is the probability that he will draw a black sock and then a red sock, P(black, then red)?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

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
6

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
7

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
8

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
9

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}.
10

The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distribution below. What is the probability that a worker chosen at random works at least 8 hours?

Question illustration
A
0.62
B
0.78
C
0.84
D
0.96
11

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%
12

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.
13

Alejandro surveyed his classmates to determine who has ever gone surfing and who has ever gone snowboarding. Let A be the event that the person has gone surfing, and let B be the event that the person has gone snowboarding.

Question illustration
A
A and B are independent events because P(A∣B) = P(A) = 0.16.
A
A and B are independent events because P(A∣B) = P(A) = 0.75.
A
A and B are not independent events because P(A∣B) = 0.16 and P(A) = 0.75.
A
A and B are not independent events because P(A∣B) = 0.75 and P(A) = 0.16.
14

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
15

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}
16

Which of the following is a valid probability distribution?

A
Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2.
Option A
B
Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1.
Option B
C
Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1.
Option C
D
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Option D
17

two

Question illustration
P
P(A|C) =
Option P
P
P(C|B) =
Option P
P
P(A) =
Option P
P
P(C) =
Option P
P
P(B|A) =
Option P
18

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).
19

Bart found 20 quadrilaterals in his classroom. He made a Venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths (E) and those with four right angles (R).

Question illustration
2
25%
3
33%
4
40%
6
67%
20

The table below shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, X, which graph shows the probability distribution, PX(x), of a randomly chosen house?Age of HouseNumber of Houses115220325430

A
A probability distribution is shown. The probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.
Option A
B
A probability distribution is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.
Option B
C
A probability distribution is shown. The probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.
Option C
D
A probability distribution is shown. The probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.
Option D

Did you find these answers helpful?

More from this Course

Quiz
25 verified answers

Cumulative Exam

Quiz
25 verified answers

Unit Test

Quiz
25 verified answers

Unit Test