Question 1

The Multiplication Rule says that P(A and B)= P(A)× P(B).What must be true about events A and B for this rule to apply?

Accepted Answer

A) The events must be disjoint. 
B) The events must be independent. 
C) The events must be mutually exclusive. 
D) Two of the above 
A) The events must be disjoint. 
B) The events must be independent. 
C) The events must be mutually exclusive. 
D) Two of the above B

Question 2

The Addition Rule says that P(A or B)= P(A)+ P(B).What must be true about events A and B for this rule to apply?

Accepted Answer

A) The events must be disjoint. 
B) The events must be independent. 
C) The events must be mutually exclusive. 
D) Two of the above 
A) The events must be disjoint. 
B) The events must be independent. 
C) The events must be mutually exclusive. 
D) Two of the above D

Question 3

The sum of the probabilities of all possible outcomes of a trial must be 1.What rule or law is this?

Accepted Answer

A) The Law of Large Numbers 
B) The Probability Assignment Rule 
C) The Total Probability Rule 
D) The Rule of Law 
E) The Law of Averages 
A) The Law of Large Numbers 
B) The Probability Assignment Rule 
C) The Total Probability Rule 
D) The Rule of Law 
E) The Law of Averages C

Question 4

The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex.  
If a person is selected at random from the sample,find the probability that the person has blood type B.

Accepted Answer

A) 0.577 
B) 0.080 
C) 0.090 
D) 0.514 
E) 0.046 
A) 0.577 
B) 0.080 
C) 0.090 
D) 0.514 
E) 0.046

Question 5

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

Accepted Answer

A) Legitimate 
B) Not legitimate 
A) Legitimate 
B) Not legitimate

Question 6

What is the probability of an event?

Accepted Answer

A) A number between 0 and 1 that reports the likelihood of the event's occurrence 
B) A collection of outcomes 
C) A single attempt or realization of a random phenomenon 
D) Its long-run relative frequency 
E) Two of the above 
A) A number between 0 and 1 that reports the likelihood of the event's occurrence 
B) A collection of outcomes 
C) A single attempt or realization of a random phenomenon 
D) Its long-run relative frequency 
E) Two of the above

Question 7

A consumer organization estimates that 34% of the households in a particular community have one television set,39% have two sets,and 20% have three or more sets.What is the probability that a household chosen at random has no more than one television set?

Accepted Answer

A) 0.41 
B) 0.59 
C) 0.07 
D) 0.34 
E) 0.46 
A) 0.41 
B) 0.59 
C) 0.07 
D) 0.34 
E) 0.46

Question 8

Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get,but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register.The store is required to reveal (in the fine print)the distribution of discounts available.Determine whether the following probability assignment is legitimate.
Probability of ...

Accepted Answer

A) Legitimate 
B) Not legitimate 
A) Legitimate 
B) Not legitimate

Question 9

A survey revealed that 50% of people are entertained by reading books,34% are entertained by watching TV,and 16% are entertained by both books and TV.What is the probability that a person will be entertained by either books or TV?

Accepted Answer

A) 1 
B) 0.32 
C) 0.84 
D) 0.16 
E) 0.68 
A) 1 
B) 0.32 
C) 0.84 
D) 0.16 
E) 0.68

Question 10

The table shows the political affiliation of voters in one city and their positions on raising taxes.  
What is the probability that a randomly picked person votes Conservative and opposes raising taxes?

Accepted Answer

A) 0.321 
B) 0.400 
C) 0.530 
D) 0.425 
E) 0.170 
A) 0.321 
B) 0.400 
C) 0.530 
D) 0.425 
E) 0.170

Question 11

A survey of the male students at a junior college reveals that,26% play soccer regularly,22% are Latino,and half of the Latino students play soccer regularly.If a male student is selected at random,what is the probability that he is neither Latino nor a soccer player?

Accepted Answer

A) 0.89 
B) 0.52 
C) 0.63 
D) 0.26 
E) 0.41 
A) 0.89 
B) 0.52 
C) 0.63 
D) 0.26 
E) 0.41

Question 12

According to a survey conducted by an environmental organization,the probability that an eligible voter cares about environmental issues is 0.61,the probability that an eligible voter voted in the last election is 0.44 and the probability that an eligible voter both voted in the last election and cares about environmental issues is 0.30.Are caring about environmental issues and voting in the last election disjoint events?

Accepted Answer

A) Yes,the probability that a voter cares about environmental issues is the same as the probability that a voter cares about environmental issues given that they voted in the last election. 
B) No,30% both care about environmental issues and voted in the last election 
C) No,the probability that a voter voted in the last election is 0.44,but the probability that a voter voted in the last election given that they care about environmental issues is 0.49. 
D) Yes,the probability that a voter cares about environmental issues and voted in the last election is zero. 
E) Yes,because P(C or V)= P(
C) + P(V) 
A) Yes,the probability that a voter cares about environmental issues is the same as the probability that a voter cares about environmental issues given that they voted in the last election. 
B) No,30% both care about environmental issues and voted in the last election 
C) No,the probability that a voter voted in the last election is 0.44,but the probability that a voter voted in the last election given that they care about environmental issues is 0.49. 
D) Yes,the probability that a voter cares about environmental issues and voted in the last election is zero. 
E) Yes,because P(C or V)= P(
C) + P(V)

Question 13

At the horse racing track,a gambler bets on the wrong horse in a 10-horse field nine times in a row.Later,when talking to a friend,he said he was confident that he would pick the winner the next time,because he was "due to pick a winner." Comment on his reasoning.

Accepted Answer

A) This is false reasoning because he doesn't appear to be lucky. 
B) This is false reasoning because there is no Law of Averages for independent events. 
C) When there are 10 horses in a race and he has chosen the wrong horse nine times in a row,he statistically should pick a winner the next time. 
D) If he doesn't pick the winning horse the next time,he will shortly after that. 
E) None of the above apply. 
A) This is false reasoning because he doesn't appear to be lucky. 
B) This is false reasoning because there is no Law of Averages for independent events. 
C) When there are 10 horses in a race and he has chosen the wrong horse nine times in a row,he statistically should pick a winner the next time. 
D) If he doesn't pick the winning horse the next time,he will shortly after that. 
E) None of the above apply.

Question 14

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate.  
Suppose one of these people is selected at random.Compute the probability that the person is aged over 45 and has had no accidents in the past three years.

Accepted Answer

A) 0.382 
B) 0.089 
C) 0.484 
D) 0.537 
E) 0.789 
A) 0.382 
B) 0.089 
C) 0.484 
D) 0.537 
E) 0.789

Question 15

Toss a coin five times;record the number of heads.

Accepted Answer

A) {0,1,2,3,4,5},equally likely 
B) {0,1,2,3,4,5},not equally likely 
C) {1,2,3,4,5},equally likely 
D) {1,2,3,4,5},not equally likely 
E) {1,2},equally likely 
A) {0,1,2,3,4,5},equally likely 
B) {0,1,2,3,4,5},not equally likely 
C) {1,2,3,4,5},equally likely 
D) {1,2,3,4,5},not equally likely 
E) {1,2},equally likely

Question 16

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.  
Find the probability that the person was an attorney and retired before the age of 61.

Accepted Answer

A) 0.190 
B) 0.267 
C) 0.048 
D) 0.062 
E) 0.499 
A) 0.190 
B) 0.267 
C) 0.048 
D) 0.062 
E) 0.499

Question 17

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.  
Suppose one of these people is selected at random.Compute the probability that the person selected was an attorney who retired between 61 and 65.

Accepted Answer

A) 0.401 
B) 0.106 
C) 0.264 
D) 0.249 
E) 0.424 
A) 0.401 
B) 0.106 
C) 0.264 
D) 0.249 
E) 0.424

Question 18

Roll a die eight times;record the length of the longest run of sixes.

Accepted Answer

A) {0,1,2,3,4,5,6,7,8},not equally likely 
B) {0,1,2,3,4,5,6,7,8},equally likely 
C) {0,1,2,3,4,5,6},not equally likely 
D) {1,2,3,4,5,6,7,8},not equally likely 
E) {1,2,3,4,5,6},equally likely 
A) {0,1,2,3,4,5,6,7,8},not equally likely 
B) {0,1,2,3,4,5,6,7,8},equally likely 
C) {0,1,2,3,4,5,6},not equally likely 
D) {1,2,3,4,5,6,7,8},not equally likely 
E) {1,2,3,4,5,6},equally likely

Question 19

The weather reporter predicts that there is a 20% chance of snow tomorrow for a certain region.What is meant by this phrase?

Accepted Answer

A) Snow occurs 20% of the time in this region. 
B) The occurrence of snow is "truly random" and will occur 20% of the time. 
C) In circumstances "like this," snow occurs 20% of the time. 
D) 20% of the time it snows on this date. 
E) It will rain 20% of the day tomorrow. 
A) Snow occurs 20% of the time in this region. 
B) The occurrence of snow is "truly random" and will occur 20% of the time. 
C) In circumstances "like this," snow occurs 20% of the time. 
D) 20% of the time it snows on this date. 
E) It will rain 20% of the day tomorrow.

Question 20

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate.
Probability of ...

Accepted Answer

A) Legitimate 
B) Not legitimate 
A) Legitimate 
B) Not legitimate

Exam 13: From Randomness to Probability

The Multiplication Rule says that P(A and B)= P(A)× P(B).What must be true about events A and B for this rule to apply?

The Addition Rule says that P(A or B)= P(A)+ P(B).What must be true about events A and B for this rule to apply?

The sum of the probabilities of all possible outcomes of a trial must be 1.What rule or law is this?

The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex. If a person is selected at random from the sample,find the probability that the person has blood type B.

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate. Probability of ...

What is the probability of an event?

A consumer organization estimates that 34% of the households in a particular community have one television set,39% have two sets,and 20% have three or more sets.What is the probability that a household chosen at random has no more than one television set?

A survey revealed that 50% of people are entertained by reading books,34% are entertained by watching TV,and 16% are entertained by both books and TV.What is the probability that a person will be entertained by either books or TV?

The table shows the political affiliation of voters in one city and their positions on raising taxes. What is the probability that a randomly picked person votes Conservative and opposes raising taxes?

A survey of the male students at a junior college reveals that,26% play soccer regularly,22% are Latino,and half of the Latino students play soccer regularly.If a male student is selected at random,what is the probability that he is neither Latino nor a soccer player?

At the horse racing track,a gambler bets on the wrong horse in a 10-horse field nine times in a row.Later,when talking to a friend,he said he was confident that he would pick the winner the next time,because he was "due to pick a winner." Comment on his reasoning.

Toss a coin five times;record the number of heads.

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Find the probability that the person was an attorney and retired before the age of 61.

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Suppose one of these people is selected at random.Compute the probability that the person selected was an attorney who retired between 61 and 65.

Roll a die eight times;record the length of the longest run of sixes.

The weather reporter predicts that there is a 20% chance of snow tomorrow for a certain region.What is meant by this phrase?

The plastic arrow on a spinner for a child's game stops rotating to point at one of four colours that will determine what happens next.Determine whether the following probability assignment is legitimate. Probability of ...

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