The scenario in this exercise is similar to the one in Exercise 7, except the class size is smaller. Suppose that there are 15 students in your class. Each day the teacher randomly selects one student to show the others how to do the previous night’s homework. Each day, all students are eligible and equally likely to be chosen, even if they have been chosen that week already. For this exercise, you want to simulate three students being drawn, mimicking the Monday, Wednesday, Friday class schedule for this class. You want to estimate the probability that the same student will be chosen all three times in one week. You plan to simulate results for 10,000 three- day weeks. For parts (a) to (e), specify what you would answer for each of the questions to accomplish this simulation using www.randomizer.org.
a. How many sets of numbers do you want to generate?
b. How many numbers per set?
c. Number range (e. g., 1– 50).
d. Do you wish each number in a set to remain unique?
e. Do you wish to sort the numbers that are generated?
f. Suppose that the same student is chosen on all 3 days in 47 of your simulated weeks. What is your estimate of the probability that the same student will be chosen all three?
g. Use the probability rules from Chapter 14 to find the probability that the same student would be chosen all three times in one week, and compare your answer to the estimated probability in part (f).