In a certain liberal arts college with about 10,000 students, 59% are males. If two students from this college are selected at random, what is the probability that they are of the same gender?

P (S) = 0.5162 or 51.62%

the probability that they are of the same gender is 0.5162 or 51.62%

Step-by-step explanation:

The probability that the two selected students are of the same gender P (S) is;

P (S) = Probability that they are both male P (M) + probability that they are both female P (F)

P (S) = P (M) + P (F) ... 1

Given;

Proportion of male = 59% = 0.59

Proportion of female = 1-0.59 = 0.41

P (M) = 0.59*0.59 = 0.3481

P (F) = 0.41 * 0.41 = 0.1681

From equation 1;

P (S) = 0.3481 + 0.1681

P (S) = 0.5162 or 51.62%

the probability that they are of the same gender is 0.5162 or 51.62%