Exam 9: Understanding Randomness

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.

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.

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.

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.