Tuesday, January 15, 2013

A probability question

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Suppose there are N lightbulbs, K of them have defects. A technician is allowed to check n lightbulbs and it turns out that exactly k defected ones among those checked.
  1. Given N,K,n, what is the probability mass function (PMF) for k? What is the expected value?
  2. Given N,n,k, what is the probability mass function (PMF) for K? What is the expected value?

A somewhat similar question is:
Suppose there are N lightbulbs, K of them have defects. A technician is allowed to check n lightbulbs. What is the probability that he can find out all the defected?