Probabilities of draws without replacement

Question

A history class is comprised of 6 female and 9 male students. If the instructor of the class randomly chooses 10 students from the class for an oral exam, what is the probability that 4 female students and 6 male students will be selected? Round your answer to 3 decimal places.

Answer 1

This is a hypergeometric probability. Population size N=15, sample size n=10, and if we define a "success" to mean "female", then K=6 successes are present in the population. The desired number of successes in the sample is k=4. Now use the hypergeometric pmf to find the desired probability.