Answer to Question #120482 in Electric Circuits for pk

Question #120482
In a sample of pistons manufactured in a factory, it is seen that 10% of the pistons
are defective. What is the probability that in a batch of 10 pistons no more than two
pistons, are defective?
1
Expert's answer
2020-06-08T10:28:08-0400

The probability of detecting a defective pistons in one test is p=0.1p=0.1 then using Bernoully formula p=p10(0)+p10(1)+p10(2)p=p_{10}(0)+p_{10}(1)+p_{10}(2) where

p10(0)=10!0!10!0.100.9100.35,p10(1)=10!1!9!0.110.990.39p_{10}(0)=\frac{10!}{0!10!}0.1^00.9^{10}\approx0.35 , p_{10}(1)=\frac{10!}{1!9!}0.1^10.9^9\approx0.39

p10(2)=10!2!8!0.120.980.19p_{10}(2)=\frac{10!}{2!8!}0.1^20.9^8\approx0.19 then p=0.93p=0.93


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