In a university class, 30 students are psychology majors, 40 are sociology majors, 28 are psychobiology majors, and 2 are home economics majors. Each major has equal numbers of males and females. Round your answers to two decimal places except where noted.

a. If two students are randomly selected, what is the probability that both are majoring in psychobiology?

b. If one student is randomly selected, what is the probability that the student is a male given that the student is a home economics major?

c. If three sociology majors are randomly selected, what is the probability that all will be males?

d. If one student is randomly selected from the entire class roster, what is the probability that the student will be both a female and a sociology major?

e. If four students are randomly selected, what is the probability that all will be either psychology or psychobiology majors given that all are females?

f. If three students are randomly selected from the entire class roster, what is the probability that the first two will be female psychobiology majors and the third will be a male psychology major? Round the answer to three decimal places.