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bighippo
02-02-2006, 01:23 PM
I need help with this question:
A computer company receives large shipments of microprocessors. It must ensure that the proportion of them that are defective are small. Suppose the computer company tests 5 mircoprocessors out of a very large shipment and if at least 1 of them is defective the shipment will be returned. If the mircroprocessors shipment contains 10% defective mircoprocessors, calculate the probability that the entire shipment will be returned.

Thanks

JohnM
02-02-2006, 02:31 PM
This can be done as a binomial probability problem.

p = P(defective) = 0.10
q = P(good) = 0.90

n = number of sampled microprocessors
r = number of defective microprocessors in the sample

If r >= 1, then the whole shipment is returned.

From the axioms of probability (complementary events):

P(A') = 1 - P(A)

so, therefore P(r >= 1) = 1 - P(r = 0)

Use the binomial formula to find P(r = 0), then subtract it from 1.

There's a post in the Examples section entitled Binomial Probabilities that shows how to use the formula.