A student is applying to nine graduate schools. She knows that they are all equally selective but

figures that there is an independent random element in each school's selection process, so by

applying to more schools she has a greater probability of getting into at least one.

She is uncertain about her chances partly because she is uncertain about what kinds of essays might

be distinctively impressive in attracting the attention of admissions officers who read many hundreds of essays per year. Given the rest of her credentials, the student believes that if her

application essay was distinctively impressive, then at each school she would have a probability

0.25 of being admitted, independent of how the other schools responded to her application. But if

she knew that her application essay was not distinctively impressive, then she would figure that at

each school, she would have a probability 0.05 of being admitted, independent of how the other

schools responded to her application.

Because of her uncertainty about the kind of essay that would be distinctively impressive to

admissions officers, she has actually drafted two different application essays. Essay #1 focuses on

her experiences in the Peace Corps after college while essay #2 focuses on her experiences as head

of student laundry services during college. If either essay really is distinctively impressive, then it

would have this intrinsic property wherever it was sent. She does not feel sure about the quality of

either essay, but she is more optimistic about essay #1. In her beliefs, there is probability 0.5 that

essay #1 is a distinctively impressive essay, and there is probability 0.3 that essay #2 is a

distinctively impressive essay, each independent of the other.

Although the student would be very glad to attend any of these nine schools, she has preferences.

Three of the schools are somewhat less preferred than the other six because of their geographic

locations. She decides to use essay #1 in the applications to her six more-desired schools, but is

undecided about what to do with the applications for the three less-desired schools. She could use

the same essay #1 for these three schools as well, or instead use essay #2 in her applications to

these three schools.

Question (1). Complete the simulation model provided in the template to study this situation. You

can use data from approximate 1,000 simulations to estimate answers to the following questions

(2) through (4). (You may also want to use COUNTIF and/or COUNTIFS function to facilitate

your calculations.) (10 points)

Question (2). What is the probability that she will be rejected by all of her six more-desired

schools when she uses essay #1 in each of these applications? (3 points)

Question (3). What would be the conditional probability of essay #1 being distinctively impressive

given that she was rejected by all six of the more-desired schools? (3 points)

Question (4). If she also used essay #1 in her applications to the three less-desired schools, then

what would be her conditional probability of getting accepted by at least one of these three schools

with essay #1, given that she was rejected by all of the six more-desired schools? (3 points)

Question (5). If she instead used essay #2 in the applications to the three less-desired schools,

then what would be her conditional probability of getting accepted by at least one of

these three schools with essay #2, given that she was rejected by all of the six more-desired

schools (with the other essay)? (3 points)

Question (6). Based on your estimation, what advice would you give to this student regarding

her application? Please justify your answer if necessary. (3 points)