On a certain day, a cheese packaging facility packaged 500 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results. \[\begin{array} { c c c } \hline & \text { Minor Flaw } & \text { No Minor Flaw } \\ \hline \text { Major Flaw } & 24 & 38 \\ \text { No Major Flaw } & 51 & 387 \\ \hline \end{array}\] Find the probability that randomly chosen cheese package has a major flaw.

A) 0.16 B) 0.048 C) 0.124 D) 0.076 A) 0.16 B) 0.048 C) 0.124 D) 0.076

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. $\begin{array} { c c } \hline \text { Response } & \text { Number } \\ \hline \text { Very satisfied } & 694 \\ \text { Somewhat satisfied } & 4015 \\ \text { Dissatisfied } & 5671 \\ \hline \text { Total } & 10,380 \end{array}$ What is the probability that a sampled person was only somewhat satisfied or dissatisfied with government's spending?

A) 0.067 B) 0.072 C) 0.928 D) 0.933 A) 0.067 B) 0.072 C) 0.928 D) 0.933

A survey asked 33,083 homeowners how many pets they owned. The results were as follow $\begin{array} { c c } \hline \text { Number of Pets } & \text { Number of Homeowners } \\ \hline 0 & 5476 \\ 1 & 11229 \\ 2 & 10546 \\ 3 & 5147 \\ 4 \text { or more } & 685 \\ \hline \text { Total } & 33,083 \end{array}$ What is the probability that a sampled homeowner has more than 1 pet?

A) 0.505 B) 0.495 C) 0.166 D) 0.176 A) 0.505 B) 0.495 C) 0.166 D) 0.176

On a certain day, a cheese packaging facility packaged 480 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results. $\begin{array} { c c c } \hline & \text { Minor Flaw } & \text { No Minor Flaw } \\ \hline \text { Major Flaw } & 16 & 30 \\ \text { No Major Flaw } & 60 & 374 \\ \hline \end{array}$ Find the probability that randomly chosen cheese package has a flaw (major or minor).

A) 0.779 B) 0.254 C) 0.188 D) 0.221 A) 0.779 B) 0.254 C) 0.188 D) 0.221

There are 29,735 undergraduate students enrolled at a certain university. The age distribution is as follows: \[\begin{array} { c c } \hline \text { Age Range } & \text { Number } \\ \hline 13 - 14 & 5 \\ 15 - 17 & 280 \\ 18 - 22 & 12,050 \\ 23 - 30 & 10,931 \\ 31 \text { and up } & 6469 \\ \hline \text { Total } & 29,735 \end{array}\] What is the probability that a student is less than 18 years old?

A) 0.0096 B) 0.0094 C) 0.218 D) 0.00017 A) 0.0096 B) 0.0094 C) 0.218 D) 0.00017

A poll was taken of 14,292 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. $\begin{array} { c c c c } \hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \\ \hline \text { High School or Less } & 3594 & 2729 & 6323 \\ \text { Bachelor's Degree } & 3245 & 3652 & 6897 \\ \text { Master's Degree } & 566 & 401 & 967 \\ \text { Ph.D. } & 63 & 42 & 105 \\ \hline \text { Total } & 7468 & 6824 & 14,292 \end{array}$ A person is selected at random. Compute the probability that the person is male or has a Ph.D.

A) 0.523 B) 0.525 C) 0.008 D) 0.530 A) 0.523 B) 0.525 C) 0.008 D) 0.530

Exam 5: Discrete Probability Distributions

On a certain day, a cheese packaging facility packaged 500 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results. Minor Flaw No Minor Flaw Major Flaw 24 38 No Major Flaw 51 387 Find the probability that randomly chosen cheese package has a major flaw.

(Multiple Choice)

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Question 41

Let A and B be events with P(A)=0.7, P(B)=0.5 , and P(B / A)=0.4 . Find P(A and B) .

(Multiple Choice)

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Question 42

A Karate club consists of 46 persons holding a black belt (highest rating), 52 persons holding a brown belt (middle rating), and 95 persons holding a purple belt (lowest rating). What is the probability that a randomly-selected club member holds a brown belt or a purple belt?

(Multiple Choice)

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Question 43

On a recent Saturday, a total of 1062 people visited a local library. Of these people, 233 were under age 10, 493 were aged 10–18, 168 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years old?

(Multiple Choice)

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Question 44

What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.

(Multiple Choice)

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Question 45

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below. Response Number Very satisfied 694 Somewhat satisfied 4015 Dissatisfied 5671 Total 10,380 What is the probability that a sampled person was only somewhat satisfied or dissatisfied with government's spending?

(Multiple Choice)

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Question 46

Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers.Suppose that $P ( E ) = 0.18 , P ( B ) = 0.18$ , and $P ( E$ and $B ) = 0.12$ . Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both

(Multiple Choice)

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Question 47

A lot of 1000 components contains 200 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find $P ( B \mid A )$

(Multiple Choice)

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Question 48

In a poll of 724 university students, 311 said that they were opposed to legalizing marijuana. Estimate the percentage of students who oppose legalizing marijuana.

(Multiple Choice)

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Question 49

A survey asked 33,083 homeowners how many pets they owned. The results were as follow Number of Pets Number of Homeowners 0 5476 1 11229 2 10546 3 5147 4 or more 685 Total 33,083 What is the probability that a sampled homeowner has more than 1 pet?

(Multiple Choice)

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Question 50

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are the same ("AA", "BB" or "CC"). [Hint: List all the outcomes of the sample space first.]

(Multiple Choice)

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Question 51

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(8)

(Multiple Choice)

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Question 52

On a certain day, a cheese packaging facility packaged 480 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results. Minor Flaw No Minor Flaw Major Flaw 16 30 No Major Flaw 60 374 Find the probability that randomly chosen cheese package has a flaw (major or minor).

(Multiple Choice)

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Question 53

A fair die is rolled two times. What is the probability that both rolls are 3?

(Multiple Choice)

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Question 54

A lot of 1000 components contains 150 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(A)

(Multiple Choice)

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Question 55

There are 29,735 undergraduate students enrolled at a certain university. The age distribution is as follows: Age Range Number 13-14 5 15-17 280 18-22 12,050 23-30 10,931 31 and up 6469 Total 29,735 What is the probability that a student is less than 18 years old?

(Multiple Choice)

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Question 56

A poll was taken of 14,292 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. Education Level Male Female Total High School or Less 3594 2729 6323 Bachelor's Degree 3245 3652 6897 Master's Degree 566 401 967 Ph.D. 63 42 105 Total 7468 6824 14,292 A person is selected at random. Compute the probability that the person is male or has a Ph.D.

(Multiple Choice)

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Question 57

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). List all the outcomes of the sample space.

(Multiple Choice)

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Question 58

For the event described below, which of the following represents the complement of the event. A sample of 471 software DVDs was selected. Exactly 34 of these were defective.

(Multiple Choice)

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Question 59

Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = 0.08. Are A and B independent?

(True/False)

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(48)

Question 60

Let A and B be events with P(A)=0.7, P(B)=0.5 , and P(B / A)=0.4 . Find P(A and B) .

A Karate club consists of 46 persons holding a black belt (highest rating), 52 persons holding a brown belt (middle rating), and 95 persons holding a purple belt (lowest rating). What is the probability that a randomly-selected club member holds a brown belt or a purple belt?

On a recent Saturday, a total of 1062 people visited a local library. Of these people, 233 were under age 10, 493 were aged 10–18, 168 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years old?

What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.

A lot of 1000 components contains 200 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find $P ( B \mid A )$

In a poll of 724 university students, 311 said that they were opposed to legalizing marijuana. Estimate the percentage of students who oppose legalizing marijuana.

A survey asked 33,083 homeowners how many pets they owned. The results were as follow Number of Pets Number of Homeowners 0 5476 1 11229 2 10546 3 5147 4 or more 685 Total 33,083 What is the probability that a sampled homeowner has more than 1 pet?

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(8)

A fair die is rolled two times. What is the probability that both rolls are 3?

A lot of 1000 components contains 150 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(A)

There are 29,735 undergraduate students enrolled at a certain university. The age distribution is as follows: Age Range Number 13-14 5 15-17 280 18-22 12,050 23-30 10,931 31 and up 6469 Total 29,735 What is the probability that a student is less than 18 years old?

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). List all the outcomes of the sample space.

For the event described below, which of the following represents the complement of the event. A sample of 471 software DVDs was selected. Exactly 34 of these were defective.

Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = 0.08. Are A and B independent?

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Probability

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Inferences on Two Samples

Tests With Qualitative Data

Correlation and Regression

Statistical Analysis Questions in ANOVA and Rank-Sum Test

Filters

Exam 5: Discrete Probability Distributions

Let A and B be events with P(A)=0.7, P(B)=0.5 , and P(B / A)=0.4 . Find P(A and B) .

A Karate club consists of 46 persons holding a black belt (highest rating), 52 persons holding a brown belt (middle rating), and 95 persons holding a purple belt (lowest rating). What is the probability that a randomly-selected club member holds a brown belt or a purple belt?

On a recent Saturday, a total of 1062 people visited a local library. Of these people, 233 were under age 10, 493 were aged 10–18, 168 were aged 19–30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years old?

What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.

A lot of 1000 components contains 200 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(B∣A)P ( B \mid A )P(B∣A)

In a poll of 724 university students, 311 said that they were opposed to legalizing marijuana. Estimate the percentage of students who oppose legalizing marijuana.

A survey asked 33,083 homeowners how many pets they owned. The results were as follow Number of Pets Number of Homeowners 0 5476 1 11229 2 10546 3 5147 4 or more 685 Total 33,083 What is the probability that a sampled homeowner has more than 1 pet?

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(8)

A fair die is rolled two times. What is the probability that both rolls are 3?

A lot of 1000 components contains 150 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(A)

There are 29,735 undergraduate students enrolled at a certain university. The age distribution is as follows: Age Range Number 13-14 5 15-17 280 18-22 12,050 23-30 10,931 31 and up 6469 Total 29,735 What is the probability that a student is less than 18 years old?

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). List all the outcomes of the sample space.

For the event described below, which of the following represents the complement of the event. A sample of 471 software DVDs was selected. Exactly 34 of these were defective.

Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = 0.08. Are A and B independent?

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Probability

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Inferences on Two Samples

Tests With Qualitative Data

Correlation and Regression

Statistical Analysis Questions in ANOVA and Rank-Sum Test

Filters

A lot of 1000 components contains 200 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find $P ( B \mid A )$