Deck 9: Understanding Randomness

Question 1

Suppose that there are two candidates for the president of your school's student government,Candidate A and Candidate B.We believe that Candidate A has about a 52% of the votes of the student body.However,you're worried that only 1000 students will show up to vote.How often will Candidate A lose in this situation? To find out,you set up a simulation.Describe how you will simulate a component and its outcomes.

A)The component is one voter voting.An outcome is a vote for Candidate A.Use three random digits,giving 000-599 a vote for Candidate A and 600-999 as no vote
B)The component is one hundred voters voting.An outcome is a vote for Candidate A.Use one random digit,giving 0-5 as vote for Candidate A and 6-9 as no vote.
C)The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-519 as a vote for Candidate A and 520-999 as a vote for Candidate B.
D)The component is ten voters voting.An outcome is a vote yes or no for the referendum.Use two random digits,giving 00-51 as a vote for Candidate A and 52-99 as a vote for Candidate B.
E)The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-520 as a vote for Candidate A and 521-999 as a vote for Candidate B.

Answer 1

The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-519 as a vote for Candidate A and 520-999 as a vote for Candidate B.

Question 2

Computers generate pseudorandom numbers.Can these numbers be used as random numbers? Why or why not?

A)No.Only truly random numbers can be used in statistics.
B)Yes.They are virtually indistinguishable from truly random numbers.
C)Yes,so long as the program that generates them does not allow the repetition of numbers in back-to-back sequence.
D)No,because they are generated in a fixed sequence.
E)Yes,so long as the program that generates them ensures that all of the prospective numbers are eventually used.

Answer 2

Yes.They are virtually indistinguishable from truly random numbers.

Question 3

Criticize the following simulation: A student simulates the outcome of a basketball player's 3-point shot by letting 0 = missed shot and 1 = made shot.

A)The simulation will not model the real situation.The simulation fails to account for the type of defense employed by the opposing team.
B)The simulation should model the real situation.
C)The simulation probably will not model the real situation.The simulation assumes that the player makes 50% of his 3-point shots,which is probably unrealistic.
D)The simulation probably will not model the real situation.The shooter's accuracy on a given day might be affected by an injury or illness.
E)The simulation cannot model the real situation.Shooting accuracy varies from day to day,so the real situation is inherently unpredictable.

Answer 3

The simulation probably will not model the real situation.The simulation assumes that the player makes 50% of his 3-point shots,which is probably unrealistic.

Question 4

Suppose that there are two candidates for the president of your school's student government,Candidate A and Candidate B.We believe that Candidate A has about a 52% of the votes of the student body.However,you're worried that only 1000 students will show up to vote.How often will Candidate A lose in this situation? To find out,you set up a simulation.Describe the response variable.

A)The response variable is the total number of students who vote.
B)The response variable is the vote of one random voter.
C)The response variable is the number of votes for Candidate A.
D)The response variable is whether Candidate A loses or not.
E)The response variable is the number of votes for Candidate B.

Question 5

When drawing five cards randomly from a deck,which is more likely,a royal flush or a full house? A royal flush is the five highest cards of a single suit.A full house is three of one denomination and two of another.How could you simulate 5-card hands? Once you have picked one card,you cannot pick that same card again.Describe how you will simulate a component and its outcomes.

A)The component is picking five cards.An outcome is the suit and denomination of the cards.You could use the digits 01-52 for the 52 different cards,ignoring 00 and 53-99,or you could use a single digit 1,2,3,or 4 for the suit and then 01-13 for the denomination (ignoring 1,5-9 for suits,and 00,14-99 for denominations).
B)The component is picking a single card.An outcome is the suit and denomination of the card.You could use the digits 01-52 for the 52 different cards,ignoring 00 and 53-99,or you could use a single digit 1,2,3,or 4 for the suit and then 01-13 for the denomination (ignoring 1,5-9 for suits,and 00,14-99 for denominations).
C)The component is picking a single card.An outcome is the denomination of the card.You could use the digits 01-52 for the 52 different cards,ignoring 00 and 53-99,or you could use a single digit 1,2,3,or 4 for the suit and then 01-13 for the denomination (ignoring 1,5-9 for suits,and 00,14-99 for denominations).
D)The component is picking five cards.An outcome is the denomination of the cards.You could use the digits 01-52 for the 52 different cards,ignoring 00 and 53-99,or you could use a single digit 1,2,3,or 4 for the suit and then 01-13 for the denomination (ignoring 1,5-9 for suits,and 00,14-99 for denominations).
E)The component is picking a single card.An outcome is the suit of the card.You could use the digits 01-52 for the 52 different cards,ignoring 00 and 53-99,or you could use a single digit 1,2,3,or 4 for the suit and then 01-13 for the denomination (ignoring 1,5-9 for suits,and 00,14-99 for denominations).

Question 6

Criticize the following simulation: A student uses a random number from 1 to 13 to simulate the value of a card drawn at random from a standard deck of playing cards.

A)The simulation will not model the real situation.The simulation should use random numbers from 1 to 12.
B)The simulation will not model the real situation.In reality,there are less "face" cards than cards with numbers.
C)The simulation might not model the real situation.The deck may not be shuffled,in which case the real situation may not be random.
D)No criticism.The simulation should model the real situation.
E)The simulation will not model the real situation.The simulation must also account for the card's suit.

Question 7

Criticize the following simulation: A student uses a random number from 5 to 13 to simulate the shoe sizes of a population of females.

A)The simulation will not model the real situation.It will predict too many small sizes and too many large sizes.Extremes in foot size are not all that common.
B)The simulation will not model the real situation.Some females have foot sizes that fall outside of the range.
C)The simulation will not model the real situation.The shoes size of a particular female is unpredictable and cannot be modeled.
D)The simulation will not model the real situation.To accurately model the population,the simulation should also account for the foot width.
E)The simulation should model the real situation.

Question 8

Is the roll of a fair die random? Why or why not?

A)Yes.You can predict the outcome beforehand.
B)No.You can usually predict the outcome on one of six attempts.
C)Yes.You cannot predict the outcome beforehand.
D)No.There is always a bias in a person's rolling technique.
E)No.A 3 or 4 is the most likely outcome.

Question 9

What is the minimum number of times that an ordinary deck of playing cards must be shuffled to make the deck random?

A)7
B)1
C)2
D)8
E)It cannot be made random.

Question 10

When drawing five cards randomly from a deck,which is more likely,a royal flush or a full house? A royal flush is the five highest cards of a single suit.A full house is three of one denomination and two of another.How could you simulate 5-card hands? Once you have picked one card,you cannot pick that same card again.Describe the response variable.

A)The response variable is whether the hand had a royal flush or a full house.
B)The response variable is whether the hand had a full house.
C)The response variable is whether the hand had neither a royal flush nor a full house.
D)The response variable is whether the hand had a royal flush.
E)The response variable is whether the hand had a royal flush,a full house,or neither.

Question 11

You take a surprise quiz in your astronomy class with 12 multiple-choice questions.You estimated that you would have about a 80% chance of getting any individual question correct.What are your chances of getting them all right? Your simulation should use at least 20 runs.

A)9.6
B)429,981,696
C)96
D)7.3003721
E)0.06871948

Question 12

When drawing five cards randomly from a deck,which is more likely,a royal flush or a full house? A royal flush is the five highest cards of a single suit.A full house is three of one denomination and two of another.How could you simulate 5-card hands? Once you have picked one card,you cannot pick that same card again.Describe how you will simulate a trial.

A)A trial is a single five-card hand.Use five sets of random numbers,ignoring repeated cards.
B)A trial is a single card.Use random numbers,ignoring repeated cards.
C)A trial is a single five-card hand.Use one set of random numbers,ignoring repeated cards.
D)A trial is five-card hands,dealt until the deck is completely dealt.Use five sets of random numbers,ignoring repeated cards.
E)A trial is a single five-card hand.Use five sets of random numbers.

Question 13

A person with type O-negative blood can donate blood to anyone who needs it,regardless of blood type.About 7% of the U.S.population has type O-negative blood.Your workplace is hosting a blood drive this afternoon.How many potential donors do you expect they will have to examine in order to get 3 units of type O-negative blood?

A)2187 people
B)43 people
C)21 people
D)343 people
E)0.21 people

Question 14

In order to illustrate the basic economic and psychological dynamics involved in purchasing life insurance,one can create a very simple game with a sack,one black marble,and three white marbles.In this game,the four marbles are placed in the sack,and the player must pay a "premium" of $5 for each draw he makes from the sack.The previously-drawn marbles are not returned to the sack so,if he keeps playing,the player is guaranteed to win the $12 award eventually (but at what cost?!).Use a simulation to predict the average cost to win the $12 assuming the player continues playing until he gets the black marble.Use 30 simulation runs,letting a random number give the number of draws to obtain the black marble on a particular run.

A)About $20.50
B)About $12.50
C)About $5.00
D)About $17.00
E)About $15.50

Question 15

You are planning to take the test to be certified to administer CPR.Your teacher has told you that only 35% of candidates pass the test the first time.For those who fail the test on the first try,41% pass on their second attempt.Estimate the percentage of those tested who still are not certified after two attempts.Your simulation should use at least 20 runs.

A)21%
B)38%
C)76%
D)69%
E)14%

Question 16

Suppose that there are two candidates for the president of your school's student government,Candidate A and Candidate B.We believe that Candidate A has about a 52% of the votes of the student body.However,you're worried that only 1000 students will show up to vote.How often will Candidate A lose in this situation? To find out,you set up a simulation.Describe how you will simulate a trial.

A)A trial is 100 votes.Examine 1,000 2-digit random numbers and count how many people voted for Candidate B.That number wins that trial.
B)A trial is 1,000 votes.Examine 1,000 3-digit random numbers and count how many people voted for each candidate.Whoever gets the majority of votes wins that trial.
C)A trial is 100 votes.Examine 100 2-digit random numbers and count how many people voted for each candidate.Whoever gets the majority of votes wins that trial.
D)A trial is 10 votes.Examine 10 1-digit random numbers and count how many people voted for each player.Whoever gets the majority of votes wins that trial.
E)A trial is 1,000 votes.Examine 1,000 3-digit random numbers and only count how many people voted for Candidate A.That number wins that trial.

Question 17

A surprise quiz was given yesterday in your biology class with 8 multiple choice questions.A classmate who took it claimed to have guessed on every question,but got them all correct.Each question had 5 possible answers.Should you believe him? Explain,basing your argument on a simulation involving at least 10 runs.

A)No,the possibility of that happening is very small,about 1.51571657.
B)Yes,it is likely.
C)It is hard to tell.The simulation would need to have more than 10 runs.
D)No,the possibility of that happening is very small,about 0.00000256.
E)Yes,it is possible.

Question 18

For a particular miniature golf hole,the chance of getting a hole-in-one is only 18%.The chance of sinking any subsequent putt is 50%.Estimate the average number of putts for this hole.(NOTE: A hole-in-one counts as one putt.)Use 30 runs in your simulation.

A)About 3.5 putts
B)About 4.5 putts
C)About 4.0 putts
D)About 2.5 putts
E)About 1.5 putts

Question 19

For each time up at bat,a baseball player has a 70% chance of making an out,a 10% chance of getting walked,and a 20% chance of getting a hit.Estimate the probability that,out of 5 at-bats,the player gets at least one hit.Use 30 simulation runs.

A)About 90%
B)About 20%
C)About 30%
D)100%
E)About 70%

Question 20

Criticize the following simulation: A student simulates math test scores by choosing a random number between 0 and 100.

A)The simulation should model the real situation.
B)The simulation probably will not model the real situation.For example,the simulation will predict just as many scores between 10 and 20 as between 70 and 80.In reality,the distribution of grades will not be so uniform.
C)The simulation probably will not model the real situation.Most students dislike math.
D)The simulation cannot model the real situation.The test performance of an individual student is inherently unpredictable.
E)The simulation will not model the real situation.It fails to account for the amount of time each student spent studying for the exam.

Question 21

A university in your region estimates that graduating average of high school students who apply for admission to a particular university program can be described by a Normal model with a mean of 82% and a standard deviation of 5%.The staff in admissions opens the applications at random looking for 10 applicants with averages above 85%.How many applications do you think the staff will need to open?

A)About 36 applications
B)About 21 applications
C)About 10 applications
D)About 28 applications
E)About 14 applications

Question 22

Five men and four women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that the last person interviewed will be a man.Your simulation should use at least 10 runs.

A)1
B) $\frac { 5 } { 9 }$
C) $\frac { 4 } { 9 }$
D)0
E) $\frac { 1 } { 9 }$

Question 23

Eight men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that the first person interviewed will be a woman.Your simulation should use at least 10 runs.

A) $\frac { 1 } { 11 }$
B)1
C) $\frac { 3 } { 11 }$
D)0
E) $\frac { 5 } { 11 }$

Question 24

The lengths of long distance phone calls placed on a cell phone can be described by a Normal model with a mean of 7 minutes and a standard deviation of 2 minutes.If one call is randomly selected from wireless phone company records,what is the probability that it will have lasted more than 11 minutes?

A)0.0977
B)0.23
C)0.977
D)0.023
E)0.98

Question 25

Six men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that all the women will be interviewed first.Your simulation should use at least 10 runs.

A) $\frac { 1 } { 56 }$
B) $\frac { 1 } { 84 }$
C) $\frac { 1 } { 14 }$
D) $\frac { 1 } { 28 }$
E) $\frac { 2 } { 3 }$

Question 26

What is the probability that Jennifer will have two sons out of her three children? Assume that boy and girl babies are equally likely.Disregard the likelihood that there are more male births and that there is a higher infant mortality rate for boys.Your simulation should use at least 10 runs.

A) $\frac { 1 } { 4 }$
B) $\frac { 3 } { 8 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 5 } { 8 }$
E) $\frac { 1 } { 8 }$