When a university sends out an offer of a place on an MBA program, it requires the applicant to respond to the offer within four weeks. The applicant may accept the offer within four weeks (in which case she or he is automatically admitted into the program), or reject the offer, or accept the offer after more than four weeks. If the applicant accepts the offer after more than four weeks, there is a 0.5 probability that he or she is admitted into the program. If the applicant accepts the offer, she or he may or may not actually arrive at the start of the academic year to take the MBA program. From experience over the past five years, a business school has found that the associated probabilities are as in the table. The business school has decided to improve its MBA program and the table also contains estimates of the corresponding probabilities for the new program, which will be offered for the first time next year.

a) What method of probability assessment was used to estimate the probabilities for the existing MBA program?

b) What method of probability assessment was used to estimate the probabilities for the new MBA program?

c) Suppose the university has sent out an offer to an applicant. Which of the probabilities in the question are conditional upon other events (i.e., other than the university sending the offer)? Identify which events they are dependent upon.

d) The university sends out an offer of a place in its existing MBA program. What is the probability that the applicant will arrive at the start of the academic year to take the program?

e) The university sends out an offer of a place in its new MBA program. What is the probability that the applicant will arrive at the start of the academic year to take the program?

Transcribed Image Text:

Probabilities New MBA Existing MBA Program Program Accept offer within four weeks 0.61 0.8 Accept offer after more than 0.12 0.1 four weeks Reject offer 0.27 0.1 Arrive at the start of the academic year 0.92 0.95