Question

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of nine syringes taken from the batch. Suppose the batch contains 5% defective syringes.

What is the probability that the batch will be accepted? (Round your answer to three decimal places.)

Answer 1

So we want to find:\[
\Pr(X\lt 2) = \Pr(X=0)+\Pr(X=1)
\]

Answer 2

\[\large
\Pr(X=0) = \binom{9}{0}(1-0.05)^9(0.05)^0 =(1-0.05)^9
\]\[\large
\Pr(X=1) =\binom{9}{1} (1-0.05)^8(0.05)^1 =9 (1-0.05)^8(0.05)^1
\]