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

it would be a on edgenuit y

the diagram below is your final answer