Question

A random sample of size 12 is taken without replacement from a lot of 100 items that contains 8 defectives.

(a) Find the probability that there are exactly two defectives in the sample.'

(b) Find the probability that there are two or fewer defectives in the sample

Answer #1

**Solution:**

(a) In this problem, there are some 100 items out of which 8 are
defective. A sample of 12 is taken out without replacement. The
example provided in the problem is a hypergeometric one.

It is required to obtain the probability that the lot has only two
defective item. The following formula can be used:

the probability that there are exactly two defectives in the
sample is **0.1922**

**(b)** The probability that there are two or fewer
defectives in the sample

The probability that there are two or fewer defectives in the
sample is **0.9469**

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