Quantitative Methods
posted by V .
Assume you have applied to two different universities (lets refer to them as Universities A and B) for your graduate program. In the past 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other.
a. probability that you will be accepted in both
b. probability that you will be accepted to at least one graduate program
c. probability that one and only one of the universities will accept you
d. probability that neither university will accept you

a.) You have to assume that the probability of being accepted with "similar credentials" is a random process. This may not be the case, however. Admissions committees do not roll dice. They may look for similar admission criteria that are not easily quantified. Assuming that it is random however, the probability of being accepted at both is (0.25)(0.35) = 0.0875
b.) This probability is 1 MINUS the probability of being rejected by both colleges. That equals 1  (0.75)(0.65) = 0.5125
c.) Add the probability of acceptance by A and rejection by B to the probability of acceptance by B and rejection by A. That is
(0.75)(0.35) + (0.25)(0.65) = 0.425
d.) (0.75)(0.65) = 0.4875 
thx that really helped, however for c i thought it was mutually exclusive so i added the two probabilities .25 and .35. i didn't realize that i needed to include the rejection percentage.