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 question

  1. Sep 17, 2007 #1
    This question is from Parzen (Modern Probability Theory), chapter 2, exercise 6.1

    1. The problem statement, all variables and given/known data
    Suppose that we have M urns, numbered 1 to M and M balls, numbered 1 to M. Let the balls be inserted randomly in the urns, with one ball in each urn. If a ball is put into the urn bearing the same number as the ball, a match is said to have occurred. Show that for j = 1,...,M the conditional probability of a match in the jth urn, given that there are m matches is m/M.

    2. Relevant equations
    Probability that there are exactly m matches in M urns is:
    (1/m!)* [tex]\Sigma[/tex][tex]^{M-m}_{k=0}[/tex](-1)^k * (1/k!)

    3. The attempt at a solution
    The answer doesn't make sense. Suppose that j = M. The probability that there will be a match in the Mth urn given that there are M-1 matches is 1. Not (M-1)/M.
  2. jcsd
  3. Sep 18, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    I think m is the total number of matches. You may think of it as a referee looking into each urn, then reporting m matches, without disclosing which urns had matches.
  4. Sep 19, 2007 #3
    Thanks a lot, EnumaElish!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook