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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.

- Given
*N,K,n*, what is the probability mass function (PMF) for*k*? What is the expected value? - 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?