stat help probability

Question

A room of people consists of 26 men and 29 women. If you randomly select a group of 5 people from this room, what is the probability that at most 4 of them are men?

Answer 1

We can apply the principles of a hypergeometric distribution.

Need to find probability that 0, 1, 2, 3 or 4 are men then add those probabilities together.

Total number of people is 55.

Start with probability pick 0 men as an example:

ways to pick 0 out of 26 men: C(26,0) --- number of combinations of 26 taken

ways to pick 5 out of 29 women: C(29,5)

ways to pick 5 out of 55 people: C(55,5)

probability pick 0 = C(26,0)C(29,5)/C(55,5) = 118755/3478761 = 0.034

Another example with probability pick 1 men:

ways to pick 1 out of 26 men: C(26,1)

ways to pick 4 out of 29 women: C(29,4)

ways to pick 5 out of 55 people: C(55,5)

probability pick 1 = C(26,1)C(29,4)/C(55,5) = 26*23751/3478761 = 0.178