Question

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?

Answer 1

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