Question

In: Math

Imagine that you are purchasing small lots of manufactured product. If it is very costly to...

Imagine that you are purchasing small lots of 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 3 items per lot and reject the lot if you observe 1 or more defectives.

a) If the lot contains 1 defective item, what is the probability that you will accept the lot?

b) What is the probability that you will accept the lot if it contains 2 defective items?

Expert Solution

Number of items in the lot = 10

Let X : number of defective items in the sample of 3 items

Reject the lot if X

Accept the lot if X =0; No defective items in the sample of 3 items from the lot i.e all 3 items to be non defective.

a) If the lot contains 1 defective item.

Probability of an item being defective = 1/10 = 0.1

Probability of an item being non-defective = 1-Probability of an item being defective = 1-0.1 = 0.9

Probability that you will accept the lot = Probability that all the 3 items to be non-defective = Probability of item 1 being non-defective x Probability of item 2 being non-defective x Probability of item 3 being non-defective = 0.9 x 0.9 x 0.9 = 0.729

If the lot contains 1 defective item, Probability that you will accept the lot = 0.729

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b) if a lot contains 2 defective items

Probability of an item being defective = 2/10 = 0.2

Probability of an item being non-defective = 1-Probability of an item being defective = 1-0.2 = 0.8

Probability that you will accept the lot = Probability that all the 3 items to be non-defective = Probability of item 1 being non-defective x Probability of item 2 being non-defective x Probability of item 3 being non-defective = 0.8 x 0.8 x 0.8 = 0.512

Probability that you will accept the lot, if it contains 2 defective items = 0.512

milcah answered 1 year ago

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