Question

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

Answer 1

a. .25*.35
b. .35*.75+.25*.65 + .25*.35
c.
d.

I will be happy to critique your thinking. In reality, the events are not independent, assuming the schools judge admission on nearly the same factors.

Answer 2

thx for your help, i had that for a but for b i use p(a) = 1-p(b) and for c i used P(a or b) = .25 + .35 = 60 and for d i caluculated that p(a): 1-.25 =.75 p(b): 1-.35 = .65 then i multiplied the two .75*.65=.4875 = 48.75%

I really appreciate your assistance