Exam 4: Introduction to Probability

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event A^c and what is the probability of this event?

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

An investor in Apple is worried the latest management earnings forecast is too aggressive and the company will fall short. His favorite analyst that covers Apple is going to release his report on Apple the week before the earnings announcement. Report stands for the analyst's report, and Forecast stands for the earnings announcement. What is the probability the earnings announcement is below the forecast?

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(Short Answer)

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Question 2

Correct Answer:

Verified

0.49

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability that a randomly selected customer prefers vanilla?

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

Two events can be both mutually exclusive and independent at the same time.

(True/False)

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Question 4

Based on his batting average, a baseball player has a 32.7% chance of hitting the ball on his next at bat. Find the odds against this player getting a hit.

(Essay)

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Question 5

An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire. The following are her predictions for the real estate market for the next year. • With 0.32 probability, foreclosures will increase in Las Vegas. • With 0.46 probability, foreclosures will increase in Las Vegas or the Inland Empire. • With 0.27 probability, foreclosures will increase in Las Vegas and the Inland Empire. What is the probability that foreclosures will increase in the Inland Empire given that they increased in Vegas?

(Short Answer)

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Question 6

Let P(A ∩B) = 0.3, and P(A ∩ B^c) = 0.15. Compute P(A).

(Multiple Choice)

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Question 7

Exams are approaching and Helen is allocating time to studying for exams. She thinks that with the appropriate amount of studying, she has an 80% chance of getting an A in Marketing. She also feels that she has a 60% chance of getting an A in Spanish with the appropriate amount of studying. Given the demands on her time, she feels that she has only a 45% chance of getting an A in both classes. What is the probability that Helen gets an A in at least one of her two classes?

(Short Answer)

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Question 8

The odds for encountering rain on a 500-mile car trip are three to one. What is the probability of rain on this trip?

(Multiple Choice)

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Question 9

The total probability rule is defined as P(A) = P(A ∩B) P(A ∩ B^c)

(True/False)

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Question 10

The complement of an event A, denoted by A^c, within the sample space S, is the event consisting of all outcomes of A that are not in S.

(True/False)

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Question 11

The addition rule is used to determine the probability of the union of two events occurring and is defined as a sum of the probabilities of both events.

(True/False)

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Question 12

Let P(A) = 0.6, P(B) = 0.3, and P(A ∪ B^C) = 0.1. Calculate P(A ∩B).

(Multiple Choice)

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Question 13

The union of two events A and B, denoted by A ∪ B, does not have outcomes from both A and B.

(True/False)

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Question 14

Combinations are used when the order in which different objects are arranged matters.

(True/False)

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Question 15

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?

(Multiple Choice)

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Question 16

The intersection of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ________.

(Multiple Choice)

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Question 17

The probability of a union of events can be greater than 1.

(True/False)

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Question 18

A small company that manufactures juggling equipment makes seven different types of clubs. The company wants to start an ad campaign that emphasizes the myriad combinations the avid juggler can create with the company's clubs. If a juggler wishes to juggle four clubs, each of a different type, how many different combinations of the company's clubs can he or she make?

(Multiple Choice)

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Question 19

The likelihood of Company A's stock price rising is 20%, and the likelihood of Company B's stock price rising is 30%. Assume that the returns of Company A and Company B stock are independent of each other. The probability that the stock price of at least one of the companies will rise is ________.

(Multiple Choice)

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Question 20

Showing 1 - 20 of 148

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event A^c and what is the probability of this event?

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability that a randomly selected customer prefers vanilla?

Two events can be both mutually exclusive and independent at the same time.

Based on his batting average, a baseball player has a 32.7% chance of hitting the ball on his next at bat. Find the odds against this player getting a hit.

Let P(A ∩B) = 0.3, and P(A ∩ B^c) = 0.15. Compute P(A).

The odds for encountering rain on a 500-mile car trip are three to one. What is the probability of rain on this trip?

The total probability rule is defined as P(A) = P(A ∩B) P(A ∩ B^c)

The complement of an event A, denoted by A^c, within the sample space S, is the event consisting of all outcomes of A that are not in S.

The addition rule is used to determine the probability of the union of two events occurring and is defined as a sum of the probabilities of both events.

Let P(A) = 0.6, P(B) = 0.3, and P(A ∪ B^C) = 0.1. Calculate P(A ∩B).

The union of two events A and B, denoted by A ∪ B, does not have outcomes from both A and B.

Combinations are used when the order in which different objects are arranged matters.

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?

The intersection of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ________.

The probability of a union of events can be greater than 1.

The likelihood of Company A's stock price rising is 20%, and the likelihood of Company B's stock price rising is 30%. Assume that the returns of Company A and Company B stock are independent of each other. The probability that the stock price of at least one of the companies will rise is ________.

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Exam 4: Introduction to Probability

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event Ac and what is the probability of this event?

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability that a randomly selected customer prefers vanilla?

Two events can be both mutually exclusive and independent at the same time.

Based on his batting average, a baseball player has a 32.7% chance of hitting the ball on his next at bat. Find the odds against this player getting a hit.

Let P(A ∩B) = 0.3, and P(A ∩ Bc) = 0.15. Compute P(A).

The odds for encountering rain on a 500-mile car trip are three to one. What is the probability of rain on this trip?

The total probability rule is defined as P(A) = P(A ∩B) P(A ∩ Bc)

The complement of an event A, denoted by Ac, within the sample space S, is the event consisting of all outcomes of A that are not in S.

The addition rule is used to determine the probability of the union of two events occurring and is defined as a sum of the probabilities of both events.

Let P(A) = 0.6, P(B) = 0.3, and P(A ∪ BC) = 0.1. Calculate P(A ∩B).

The union of two events A and B, denoted by A ∪ B, does not have outcomes from both A and B.

Combinations are used when the order in which different objects are arranged matters.

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?

The intersection of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ________.

The probability of a union of events can be greater than 1.

The likelihood of Company A's stock price rising is 20%, and the likelihood of Company B's stock price rising is 30%. Assume that the returns of Company A and Company B stock are independent of each other. The probability that the stock price of at least one of the companies will rise is ________.

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event A^c and what is the probability of this event?

Let P(A ∩B) = 0.3, and P(A ∩ B^c) = 0.15. Compute P(A).

The total probability rule is defined as P(A) = P(A ∩B) P(A ∩ B^c)

The complement of an event A, denoted by A^c, within the sample space S, is the event consisting of all outcomes of A that are not in S.

Let P(A) = 0.6, P(B) = 0.3, and P(A ∪ B^C) = 0.1. Calculate P(A ∩B).