Exam 10: Understanding Randomness

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.

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.

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

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.

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.

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.

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

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?

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

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

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 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?

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.

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.

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.

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 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.

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.

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.

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.