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?

Treat this almost as 2 separate problems.

P (male) = 0.40. P (two males) = (0.40) (0.40) = 0.1600.

P (female) = 0.60. P (two females) = (0.60) ^2 = 0.3600

Now add these two probabilities together: P (students are of the same gender) = 0.52