In a certain liberal arts college with about 10,000 students, 40% are males. if two students from this college are selected at random, what is the probability that they are of the same gender?

Using the binomial distribution, it is found that there is a 0.52 = 52% probability that they are of the same gender.

For each student selected, there are only two possible outcomes. Either it is a male student, or a female student. The gender of a student is independent of any other student, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.

In this problem:

Same gender is either two females, given by P(X = 0), or two males, given by P(X = 2), thus:

In which:

Then

0.52 = 52% probability that they are of the same gender.

A similar problem is given at link

step-by-step explanation: