A university scholarship committee must select two students

A university scholarship committee must select two students to receive a certain scholarship. The committee receives eight applications for the scholarships - five from male students and three from female students. The applicants are all equally qualified, so the two scholarship winners are randomly selected from the eight applicants. Let X be the number of female students who receives a scholarship. Then

A. X is not a Binomial random variable.
B. XBin(3,3/8)
C. XBin(2,3/8)
D. XBin(2,2/8)
E. XBin(2,2/3)

Solution

A. X is not a binomial random variable.

Although it is true that there are only two outcomes (male and female), the probability that a female can be chosen is not constant, as it changes when the first choice is being made.

[For example, the probability of a girl on the first try is 3/8. Now, for the second try, it becomes 2/7.]