Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic Probability Question

  1. Mar 14, 2013 #1
    Suppose I have a room of 100 people, 10 of which are women. What is the probability that a group of 5, selected at random, are all women.

    Is it (.1)^5 or is it (10/100)*(9/99)*(8/98)*(7/97)*(6/96). Or is it something else? Also any references to help me understand this question better would be greatly appreciated!
  2. jcsd
  3. Mar 14, 2013 #2


    User Avatar
    Gold Member

    Second one looks right to me
  4. Mar 15, 2013 #3


    User Avatar
    Science Advisor

    The probability, assumming each woman is equally-likely to be selected is:

    # of ways of choosing 5 women / # of ways of choosing any 5 people, which

    agrees with your second answer. The first answer is true if you had "replacement",

    i.e., if every time a woman was selected, she would go back into the pool. But

    once you select a woman I imagine you select the second, etc., from the remaining

    ones, so that the probability of selecting is not always 0.1; it changes every time

    one is selected, which is reflected in your second answer.

    BTW, the more formal way is doing the ratio: 10C5 / 100C5

    where nCm := n!/(m!(n-m)!).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook