A bin of 30 manufactured parts contains three defective parts and 27 nondefectiv

Question

A bin of 30 manufactured parts contains three defective parts and 27 nondefective parts. A sample of six parts is selected from the 30 parts. Selected parts are not replaced. That is, each part can only be selected once and the sample is a subset of the 30 parts. Does the order matter for this problem? - Justify your answer How many different samples are there of size six? How many different samples are there of size six that contain exactly two defective parts? Assume that a sample of six parts is randomly generated, what is the probability of having a sample with exactly two defective parts?

Explanation / Answer

a)

No. We only need to know how many defective and nondefective parts have we drawn, regardless of order.

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b)

There are

30C6 = 593775 samples [ANSWER]

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c)

There are 27C4 = 17550 ways to choose 4 nondefectives.

There are 3C2 = 3 ways to choose 2 defectives.

Hence, there are 17550*3 = 52650 such samples. [ANSWER]

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d)

From parts b and c,

P = 52650/593775 = 0.088669951 [ANSWER]

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