Answer to Question #120482 in Electric Circuits for pk

Question

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?

Answer 1

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

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

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