Hypergeometric Distribution homework problem

[Jamin2112]

Homework Statement

A large company employs 20 individuals as statisticians, 7 of whom are women and 13 of whom are men. No two people earn the same amount.

What is the probability that 6 of the women earn salaries below the median salary of the group?

Homework Equations

If r is the number of "successes" in a set of N element, and x is the number of success in n elements draw, then p(x) = (r choose x) ( (n - r) choose (n - x) ) / (N choose n).

The Attempt at a Solution

I'm pretty sure that I just plug & chug with N = 20, n = 10, r = 7, x = 6. But I'm not 100% sure about the logic of all this. So, we look at the 10 persons below the median, who, for all we know, are just 10 random people from the group of 20. We know that there are 7 women in the group of 20, and we want to know the probability that 6 of our 10 random persons are women. Is that right? I feel a little thrown-off by the "median" thing.

 

[EV33]

I am probably not the best source for this question but I have the same exact logic as you on this problem. The sample size is 20 (which is N). 7 out of the 20 you would consider sucesses (which is r). You are selcecting 10 people at random from the the 20 because that is how many there is below the median (which is n), and you want there to be exactly 6 successes out of the 10 (which is x). So I say plug and chug the way you have it.