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JackieLe
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.)
So we want to find:\[ \Pr(X\lt 2) = \Pr(X=0)+\Pr(X=1) \]
\[\large \Pr(X=0) = \binom{9}{0}(1-0.05)^9(0.05)^0 =(1-0.05)^9 \]\[\large \Pr(X=1) =\binom{9}{1} (1-0.05)^8(0.05)^1 =9 (1-0.05)^8(0.05)^1 \]