SOLUTION: A certain manufactured bag is visually inspected by two different quality control inspectors. When a defective bag comes through the line, the probability that it gets by the first

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Question 1099682: A certain manufactured bag is visually inspected by two different quality control inspectors. When a defective bag comes through the line, the probability that it gets by the first inspector is 0.065. Of those the get past the first inspector, the second inspector will miss six out of fifteen. What fraction of the defectives get by both inspectors?
Answer by Theo(13342) About Me  (Show Source):
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the probability of the bag getting through the first inspector is .065.

the probability of the bag that gets through the first inspector getting through the second inspector is 6/15.

the probability of the bag getting through both inspectors is therefore .065 * 6/15 = .026

assume 1000 bags to start.

on average, 6.5% of them will get through the first inspector.

that equates to 65 getting through the first inspector.

of these, 6 out of 15 will get through the second inspector.

that equates to 26 getting through the second inspector.

26 out of 1000 is equal to 2.6%.