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

A Combinatoric Probability Question

  1. Aug 30, 2005 #1
    Suppose we have infinitely many boxes and the probability of any one box is non-empty is p.
    Now if we randomly choose m boxes from them, line them up and name them as box 1, box 2,..., box m. Then for given n and k (k<n<m), what is the probability that there exist a set of n consecutive boxes that we can find k or more non-empty boxes in it?
    Anyone know how to approach this question? Thanks.
  2. jcsd
  3. Aug 30, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    let E(r) be the probaility that there are k empty boxes in the range (r,r+n-1) where r can go from 1 to m-n+1. Then we want to know


    which is inclusion exclusion principle innit?
  4. Aug 30, 2005 #3
    you can formulate the following recursion
    where f(m,n,k) is the probability that...("what you have stated")
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Combinatoric Probability Question Date
B Arranging blocks so that they fit together Jul 8, 2017
B Combinatorics problem Nov 29, 2016
I Probability involving n dice Apr 26, 2016
Probability - Combinatorics Sep 19, 2012
Conditional Probability with combinatorics Aug 22, 2009