Chapter 5.3, Problem 87E

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

Gender	Frequency
Male	17
Female	23

Two students are selected at random. Find the probability that both students are male if the selection is done

1. a. with replacement.
2. b. without replacement.
3. 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, 170 males and 230 females.

1. d. Repeat parts (a)–(c), using this hypothetical distribution of students.
2. e. In which case is there less difference between sampling without and with replacement? Explain why this is so.