AnswersConcepts in Probability and Statistics AIndependent and Mutually Exclusive Events

Independent and Mutually Exclusive Events Answers

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When a softball player gets a hit, it can be a single, double, triple, or home run. When Josephine is at bat, the probability that she hits a single is 15 percent and the probability that she hits a double is 5 percent.What is the probability that Josephine hits a single or a double when she is at bat?

A
3 percent
B
10 percent
C
20 percent
D
75 percent
2
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In a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. Each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10.If event A is choosing a king, event B is choosing a heart, and event C is choosing a jack, which Venn diagram could represent this description?

A
Circles A and B overlap, and circles B and C overlap.
Option A
B
Circles A, B, and C overlap.
Option B
C
Circle A, B, and C are shown. They do not overlap.
Option C
D
Circles A and C overlap. Circle B is to the side.
Option D
3

A bag contains eleven equally sized marbles, which are numbered. Two marbles are chosen at random and replaced after each selection.

Question illustration
A
StartFraction 10 Over 121 EndFraction
Option A
B
StartFraction 24 Over 121 EndFraction
Option B
C
StartFraction 6 Over 11 EndFraction
Option C
D
StartFraction 10 Over 11 EndFraction
Option D
4

A six-sided number cube is rolled twice.What is the probability that the first roll is an even number and the second roll is a number greater than 4?

A
One-sixth
Option A
B
One-third
Option B
C
Two-thirds
Option C
D
Five-sixths
Option D
5

A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?

A
StartFraction 5 Over 24 EndFraction
Option A
B
One-sixth
Option B
C
One-fourth
Option C
D
Five-twelfths
Option D
6

The Hawaiian language has 12 letters: five vowels and seven consonants. Each of the 12 Hawaiian letters are written on a slip of paper and placed in the bag. A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag.What is the probability that two vowels are chosen?

A
StartFraction 5 Over 72 EndFraction
Option A
B
StartFraction 25 Over 144 EndFraction
Option B
C
StartFraction 7 Over 12 EndFraction
Option C
D
Five-sixths
Option D
7

All freshmen, sophomores, juniors, and seniors attended a high school assembly. The total student attendance is shown in the table.

Question illustration
A
StartFraction 11 Over 320 EndFraction
Option A
B
StartFraction 3 Over 80 EndFraction
Option B
C
StartFraction 11 Over 40 EndFraction
Option C
D
Two-fifths
Option D
8

A bag contains eleven equally sized marbles, which are numbered.

Question illustration
A
Two-elevenths
Option A
B
Three-elevenths
Option B
C
Five-elevenths
Option C
D
Six-elevenths
Option D
9

The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table.

Question illustration
A
StartFraction 3 Over 25 EndFraction
Option A
B
StartFraction 7 Over 25 EndFraction
Option B
C
StartFraction 13 Over 25 EndFraction
Option C
D
StartFraction 17 Over 25 EndFraction
Option D
10

A bicycle manufacturer is studying the reliability of one of its models. The study finds that the probability of a brake defect is 4 percent and the probability of both a brake defect and a chain defect is 1 percent.If the probability of a defect with the brakes or the chain is 6 percent, what is the probability of a chain defect?

A
1.5 percent
B
2 percent
C
2.5 percent
D
3 percent

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