Question

Simulation and Expected Values: Yale Law School says 74% of their students pass the bar exam on their first try.

To simulate passing students, we could assign the random digits as:

00 to 49 = pass first try, 50 to 99 = fail first try

0 to 7 = pass first try, 8 to 9 = fail first try

00 to 73 = pass first try, 74 to 99 = fail first try

0 to 4 = pass first try, 5 to 9 = fail first try

The outcomes for this experiment are __________________, with a probability of ________________, and __________________, with a probability of __________________.

Answer 1

Yale Law School says 74% of their students pass the bar exam on their first try. This can be interpreted as given a randomly selected Yale Law school student, the probability that the student passes the bar exam on the first try is 0.74.

The probability that a randomly selected student fails the bar exam on the first try is

1- (The probability that a randomly selected student passes the bar exam on the first try) = 1- 0.74= 0.26

To simulate, since the probability is to the accuracy of 2 decimals, we need 100 random numbers starting from 00 to 99.

If the random number simulated is among the first 74 digits (that is between 00 to 73) then we can say that the student has passed the exam in the first try. If the number is between 74 to 99, we can say that the student has failed the exam.

To simulate passing students, we could assign the random digits as:

ans:  00 to 73 = pass first try, 74 to 99 = fail first try

ans: The outcomes for this experiment are pass first try, with a probability of 0.74, and fail first try, with a probability of 0.26.