# Probability

Suppose 3 items are inspected and if at least one defective is found, the lot will be 100% inspected. Otherwise, the lot will be passed on. How likely it is that a lot containing 5 defectives will be passed on?

### Suppose the lot size is $N$.

Suppose the lot size is $N$. The sample size $n = 3$. The lot will be passed on if none of the 5 defectives got selected to $n$. Hence,

$P = \dfrac{\displaystyle{\binom{5}{0}} \cdot \displaystyle{\binom{N - 5}{3}}}{\displaystyle{\binom{N}{3}}}$

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