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) 0.28B) 0.32C) 0.52D) 0.38
Accepted Solution
A:
Answer:the probability is 0.28Step-by-step explanation:using Bayes's theoremP(A|B)=P(A∩B)/P(B)where P(A∩B) = probability that events A and B happenP(A|B) = probability that event A happen if B already happenedP(B)= probability of event BthereforeP(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 studentP(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