Lot inspection sampling Imagine you are purchasing small lot

Lot inspection sampling. Imagine you are purchasing small lots of a manufactured product. If it is very costly to test a single item, it may be desirable to test a sample of items from the lot instead of testing every item in the lot. Suppose each lot contains 10 items. You decide to sample 4 items per lot and reject the lot if you observe 1 or more defective. If the lot contains I defective item, what is the probability that you will accept the lot? What is the probability that you will accept the lot if it contains 2 defective items?

Solution

a)

There are 10C4 ways to choose any 4 items.

There are 9C4 ways to choose 4 non defectives.

Thus,

P(accept) = 9C4 / 10C4 = 0.6 [ANSWER]

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b)

There are 10C4 ways to choose any 4 items.

There are 8C4 ways to choose 4 non defectives.

Thus,

P(accept) = 8C4 / 10C4 = 0.333333333 [ANSWER]