Question 1

Which of the following statements is true in general (i.e., always true for all situations)?

Accepted Answer

A)  P(A∪
B) = P(
A)  + P(
B)  
B)  P(A∩
B)  = P(
A)  · P(
B)  
C)  P(B∩
A)  = P(
A)  · P(B|
A)  
D)  P(B|
A)  = P(A|
B)  
A)  P(A∪
B) = P(
A)  + P(
B)  
B)  P(A∩
B)  = P(
A)  · P(
B)  
C)  P(B∩
A)  = P(
A)  · P(B|
A)  
D)  P(B|
A)  = P(A|
B)  C

Question 2

Which of the following statements is true if and only if events A and B are independent?

Accepted Answer

A)  P(A∪
B)  = P(
A)  + P(
B)  
B)  P(A∩
B)  = P(
A)  ∙ P(
B)  
C)  P(A∩
B)  = P(
A)  ∙ P 
D)    
A)  P(A∪
B)  = P(
A)  + P(
B)  
B)  P(A∩
B)  = P(
A)  ∙ P(
B)  
C)  P(A∩
B)  = P(
A)  ∙ P 
D)    B

Question 3

Suppose we know that for a particular population, the proportion of those age 65 and older who smoke is 0.21.We also know that the proportion of the same population who are younger than 65 and smoke is 0.10.What proportion of the population smokes?

Accepted Answer

A)  0.021 
B)  0.31 
C)  0.11 
D)  Need more information. 
A)  0.021 
B)  0.31 
C)  0.11 
D)  Need more information. B

Question 4

In a game of chance, two pyramid-shaped, four-sided dice (with sides 1, 2, 3, 4) are rolled and their individual totals are added.If the sum of the 2 four-sided dice exceeds 5 (result from die 1 + result from die 2 > 5), the roller wins.If the sum is 5 or less, the roller loses.What is the probability of winning on a single play?

Accepted Answer

A)  5/8 
B)  3/16 
C)  3/8 
D)  1/2 
A)  5/8 
B)  3/16 
C)  3/8 
D)  1/2

Question 5

The sum of the probabilities of all possible outcomes in a sample space is:

Accepted Answer

A)  always 0. 
B)  always between 0 and 1. 
C)  always 1. 
D)  always more than1. 
A)  always 0. 
B)  always between 0 and 1. 
C)  always 1. 
D)  always more than1.

Question 6

Suppose you deal two cards from a standard deck of 52 cards.If you replace the first card in the deck before you deal the second card, what is the probability you deal a face card (jack, queen, or king) and then an odd number (3, 5, 7 or 9)?

Accepted Answer

A)  0.071 
B)  0.72 
C)  0.75 
D)  0.77 
A)  0.071 
B)  0.72 
C)  0.75 
D)  0.77

Question 7

For any two events denoted A and B, the event A∩B is best described as:

Accepted Answer

A)  all outcomes in A or B or both. 
B)  all outcomes in both A and B. 
C)  all outcomes that are in neither A nor B. 
D)  all outcomes that are in A and not in B. 
A)  all outcomes in A or B or both. 
B)  all outcomes in both A and B. 
C)  all outcomes that are in neither A nor B. 
D)  all outcomes that are in A and not in B.

Question 8

A tree diagram is:

Accepted Answer

A)  similar to a Venn diagram and useful for visually depicting a data set. 
B)  a useful tool for graphically depicting a sample space. 
C)  vital for choosing the experimental outcome that is certain to occur in the next trial. 
D)  the only way to determine accurate probability estimates. 
A)  similar to a Venn diagram and useful for visually depicting a data set. 
B)  a useful tool for graphically depicting a sample space. 
C)  vital for choosing the experimental outcome that is certain to occur in the next trial. 
D)  the only way to determine accurate probability estimates.

Question 9

Suppose you have a group of 8 male and 4 female volunteers.How many ways are there to choose 6 of these volunteers for a treatment group?

Accepted Answer

A)  28 
B)  32 
C)  420 
D)  924 
A)  28 
B)  32 
C)  420 
D)  924

Question 10

A wildlife biology crew is tagging deer in California for a census.If, on a statewide basis, 40% of deer are males (bucks), what is the probability that the crew will randomly and independently tag three females (does) in a row, assuming the area's deer population is representative of the entire state? (Assume an infinite population.)

Accepted Answer

A)  0.216 
B)  1.2 
C)  0.064 
D)  0.180 
A)  0.216 
B)  1.2 
C)  0.064 
D)  0.180

Question 11

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. ​   ​
Based on the table, what is the probability that a person who tests negative does not have the disease?

Accepted Answer

A)  99.99% 
B)  97.7% 
C)  92.6% 
D)  6.2% 
A)  99.99% 
B)  97.7% 
C)  92.6% 
D)  6.2%

Question 12

Experts give a certain poorly performing professional sports team an 80% chance of winning at least one game during the upcoming regular season.Based on this prediction, what is the probability that the team will not win any games?

Accepted Answer

A)  4/5 
B)  0.20 
C)  0.19 
D)  0.50 
A)  4/5 
B)  0.20 
C)  0.19 
D)  0.50

Question 13

A simple event is:

Accepted Answer

A)  something that simply happens. 
B)  an event consisting of exactly one outcome. 
C)  the most basic expression of the probabilistic process. 
D)  an event that has no complex outcomes. 
A)  something that simply happens. 
B)  an event consisting of exactly one outcome. 
C)  the most basic expression of the probabilistic process. 
D)  an event that has no complex outcomes.

Question 14

S = {E1, E2, E3, E4, E5, E6}.A = {E1, E4}.If S represents an equally likely outcome experiment, then what is P(A)?

Accepted Answer

A)  1/3 
B)  2/3 
C)  1/6 
D)  We need the individual simple event probabilities to solve the problem. 
A)  1/3 
B)  2/3 
C)  1/6 
D)  We need the individual simple event probabilities to solve the problem.

Question 15

Steve has 18 black socks and 12 blue socks.Every morning he pulls a sock at random from his drawer, then pulls a second sock at random, and wears both socks, regardless of their color.What is the probability he wears mismatched socks?

Accepted Answer

A)  0.248 
B)  0.152 
C)  0.352 
D)  0.50 
A)  0.248 
B)  0.152 
C)  0.352 
D)  0.50

Question 16

Suppose S = {E1, E2, E3, E4, E5, E6}.If we define set A (a subset of S) as A = {E1, E4}, then A can be best defined as:

Accepted Answer

A)  an event. 
B)  a simple event. 
C)  the main event. 
D)  the sample space. 
A)  an event. 
B)  a simple event. 
C)  the main event. 
D)  the sample space.

Question 17

The table shows the results of an experiment used to test whether Red Dye #2 causes cancer in laboratory rats. ​   ​
Based on the table, what is the probability that a rat that was given a high dose of the dye did not have a tumor?

Accepted Answer

A)  0.13 
B)  0.30 
C)  0.70 
D)  0.43 
A)  0.13 
B)  0.30 
C)  0.70 
D)  0.43

Question 18

A listing of all the possible outcomes from an experiment using set notation is called the:

Accepted Answer

A)  experimental outcome list. 
B)  event. 
C)  sample space. 
D)  sample point. 
A)  experimental outcome list. 
B)  event. 
C)  sample space. 
D)  sample point.

Question 19

If a series of n events are known to be independent, the probability of the entire series of events occurring is:

Accepted Answer

A)  the sum of the individual event probabilities minus the intersection probability. 
B)  the product of the individual event probabilities. 
C)  always 1. 
D)  never 0. 
A)  the sum of the individual event probabilities minus the intersection probability. 
B)  the product of the individual event probabilities. 
C)  always 1. 
D)  never 0.

Question 20

Which of the following is a reasonable estimate for the probability that Thanksgiving Day in the United States will be on a Thursday this year?

Accepted Answer

A)  0 
B)  0.25 
C)  0.5 
D)  1 
A)  0 
B)  0.25 
C)  0.5 
D)  1

Which of the following statements is true in general (i.e., always true for all situations)?

Which of the following statements is true if and only if events A and B are independent?

Suppose we know that for a particular population, the proportion of those age 65 and older who smoke is 0.21.We also know that the proportion of the same population who are younger than 65 and smoke is 0.10.What proportion of the population smokes?

The sum of the probabilities of all possible outcomes in a sample space is:

Suppose you deal two cards from a standard deck of 52 cards.If you replace the first card in the deck before you deal the second card, what is the probability you deal a face card (jack, queen, or king) and then an odd number (3, 5, 7 or 9)?

For any two events denoted A and B, the event A∩B is best described as:

A tree diagram is:

Suppose you have a group of 8 male and 4 female volunteers.How many ways are there to choose 6 of these volunteers for a treatment group?

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. Based on the table, what is the probability that a person who tests negative does not have the disease?

Experts give a certain poorly performing professional sports team an 80% chance of winning at least one game during the upcoming regular season.Based on this prediction, what is the probability that the team will not win any games?

A simple event is:

S = {E1, E2, E3, E4, E5, E6}.A = {E1, E4}.If S represents an equally likely outcome experiment, then what is P(A)?

Steve has 18 black socks and 12 blue socks.Every morning he pulls a sock at random from his drawer, then pulls a second sock at random, and wears both socks, regardless of their color.What is the probability he wears mismatched socks?

Suppose S = {E1, E2, E3, E4, E5, E6}.If we define set A (a subset of S) as A = {E1, E4}, then A can be best defined as:

The table shows the results of an experiment used to test whether Red Dye #2 causes cancer in laboratory rats. Based on the table, what is the probability that a rat that was given a high dose of the dye did not have a tumor?

A listing of all the possible outcomes from an experiment using set notation is called the:

If a series of n events are known to be independent, the probability of the entire series of events occurring is:

Which of the following is a reasonable estimate for the probability that Thanksgiving Day in the United States will be on a Thursday this year?

Why Study Statistics

An Introduction to Statistics and Statistical Inference

Tables and Graphs for Summarizing Data

Numerical Summary Measures

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Confidence Intervals Based on a Single Sample

Hypothesis Tests Based on a Single Sample

Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The Analysis of Variance

Correlation and Linear Regression

Categorical Data and Frequency Tables

Nonparametric Statistics

Filters

Exam 5: Probability

Which of the following statements is true in general (i.e., always true for all situations)?

Which of the following statements is true if and only if events A and B are independent?

Suppose we know that for a particular population, the proportion of those age 65 and older who smoke is 0.21.We also know that the proportion of the same population who are younger than 65 and smoke is 0.10.What proportion of the population smokes?

The sum of the probabilities of all possible outcomes in a sample space is:

Suppose you deal two cards from a standard deck of 52 cards.If you replace the first card in the deck before you deal the second card, what is the probability you deal a face card (jack, queen, or king) and then an odd number (3, 5, 7 or 9)?

For any two events denoted A and B, the event A∩B is best described as:

A tree diagram is:

Suppose you have a group of 8 male and 4 female volunteers.How many ways are there to choose 6 of these volunteers for a treatment group?

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. ​ ​ Based on the table, what is the probability that a person who tests negative does not have the disease?

Experts give a certain poorly performing professional sports team an 80% chance of winning at least one game during the upcoming regular season.Based on this prediction, what is the probability that the team will not win any games?

A simple event is:

S = {E1, E2, E3, E4, E5, E6}.A = {E1, E4}.If S represents an equally likely outcome experiment, then what is P(A)?

Steve has 18 black socks and 12 blue socks.Every morning he pulls a sock at random from his drawer, then pulls a second sock at random, and wears both socks, regardless of their color.What is the probability he wears mismatched socks?

Suppose S = {E1, E2, E3, E4, E5, E6}.If we define set A (a subset of S) as A = {E1, E4}, then A can be best defined as:

The table shows the results of an experiment used to test whether Red Dye #2 causes cancer in laboratory rats. ​ ​ Based on the table, what is the probability that a rat that was given a high dose of the dye did not have a tumor?

A listing of all the possible outcomes from an experiment using set notation is called the:

If a series of n events are known to be independent, the probability of the entire series of events occurring is:

Which of the following is a reasonable estimate for the probability that Thanksgiving Day in the United States will be on a Thursday this year?

Why Study Statistics

An Introduction to Statistics and Statistical Inference

Tables and Graphs for Summarizing Data

Numerical Summary Measures

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Confidence Intervals Based on a Single Sample

Hypothesis Tests Based on a Single Sample

Confidence Intervals and Hypothesis Tests Based on Two Samples or Treatments

The Analysis of Variance

Correlation and Linear Regression

Categorical Data and Frequency Tables

Nonparametric Statistics

Filters

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. Based on the table, what is the probability that a person who tests negative does not have the disease?

The table shows the results of an experiment used to test whether Red Dye #2 causes cancer in laboratory rats. Based on the table, what is the probability that a rat that was given a high dose of the dye did not have a tumor?