1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Probability Q using Stirling's Formula

  1. Sep 7, 2011 #1
    Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. The group is split in half at random. What is the probability that each half contains exactly N women and N men?

    And the second part asks for a given N, set up Stirling's Formula so you can calculate the approx value for a given N.

    I am having trouble thinking how to set up this problem. I know as N gets bigger, the possible combinations increase....I'm thinking 2^n.
    I also know that the order does not matter, but with each selection you are taking removing someone from the pool of 4N people.
  2. jcsd
  3. Sep 7, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You want a _hypergeometric_ distribution here. The hypergeometric describes the following: given a population of M items, M1 of type 1 and M2 of type 2, suppose you extract a a sample of n items at random without replacement. What is the probability your sample contains exactly k items of type 1? In your case, M = 2N, M1 = M2 = N, n = N and k = N. There are standard formulas for the hypergeometric distribution.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook