Sampling and the Binomial Distribution. Following is a gender frequency distribution for students in Professor Weiss’s introductory statistics class.

Gender Frequency Male 25 Female 15 Two students are selected at random. Find the probability that both are male if the selection is done

a. with replacement.

b. without replacement.

c. Compare the answers obtained in parts

(a) and (b).

Suppose that Professor Weiss’s class had 10 times the students, but in the same proportions, that is, 250 males and 150 females.

d. Repeat parts (a)–(c), using this hypothetical distribution of students.

e. In which case is there less difference between sampling without and with replacement? Explain why this is so.