According to the record of the registrar's office at a state university, 35% of the students arefreshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. What is the probability that a randomly selected studentis a freshman who lives in a dormitory?

A) 0.28

B) 0.32

C) 0.52

D) 0.38

the probability is 0.28

Step-by-step explanation:

using Bayes's theorem

P (A|B) = P (A∩B) / P (B)

where

P (A∩B) = probability that events A and B happen

P (A|B) = probability that event A happen if B already happened

P (B) = probability of event B

therefore

P (A∩B) = P (A|B) * P (B)

if event A = selection of a student that lives in a dormitory and event B = selection of a freshmen student

P (A|B) = 0.8 (live in a dormitory knowing that is a freshmen student)

P (B) = 0.35 (freshmen student)

P (A∩B) = P (A|B) * P (B) = 0.8 * 0.35 = 0.28