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Statistics :-( can i use a binomial probability?

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data
    You've got N marbles, and N bins. one by one, a marble is randomly placed in a bin. What is the probability that there will be no marbles in a given bin.


    2. Relevant equations

    P=N!/(n1!n2!)*p^n1*q^n2 : binomial probability

    3. The attempt at a solution

    since we're only interested in whether or not a marble goes into the bin, can I use the binomial distribution? success would be when a marble is placed in a bin other than the bin of interest, and failure would be when a marble is placed in the bin of interest.

    n1=N (success), n2=0 (failure)
    p=probability of placing a single marble in a bin other than the bin of interest
    = (N-1)/N
    q=probability of placing a single marble in the bin of interest
    = 1/N

    P=N!/(N!0!)*p^N*q^0=((N-1)/N)^N

    so, what do you think? I've been doing extra stat/probability problems to help with my stat/thermo physics class and I don't have the answers to the questions...
     
  2. jcsd
  3. Mar 20, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think that's correct. The probability that any given marble doesn't fall in the bin is (N-1)/N. The probability that N of them don't is ((N-1)/N)^N.
     
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