Question

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

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

Math   Statistics-And-Probability   
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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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