The admissions office of a private university released the following data for the preceding academic year: From a pool of 3900 male applicants, 30% were accepted by the university, and 30% of these subsequently enrolled. Additionally, from a pool of 3600 female applicants, 35% were accepted by the university, and 30% of these subsequently enrolled. What is the probability of each of the following?

a. A male applicant will be accepted by and subsequently will enroll in the university?
b. A student who applies for admissions will be accepted by the university?
c. A student who applies for admission will be accepted by the university and subsequently will enroll?

a. The probability that a random male applicant is accepted and enrolls is given by the probability of a male student being accepted multiplied by the probability of a male student enrolling:

[tex]P(a) = 0.30*0.30=0.09=9\%[/tex]

b. The probability that a random student is accepted is given by the probability of a male applicant being accepted added to the probability of a female applicant being accepted

[tex]P(b) = m*0.30+f*0.35\\P(b) = 0.52*0.30+0.48*0.35\\P(b) = 0.324=32.4\%[/tex]

c. The probability that a random student is accepted and enrolls is given by the probability of a male applicant being accepted and enrolling added to the probability of a female applicant being accepted and enrolling

[tex]P(b) = m*0.30*0.30+f*0.35*0.30\\P(b) = 0.52*0.30*0.30+0.48*0.35*0.30\\P(b) = 0.0972=9.72\%[/tex]