Items are inspected for flaws by two quality inspectors. If aflaw is present, it

Question

Items are inspected for flaws by two quality inspectors. If aflaw is present, it will be detected by the first inspector withprobability 0.9, and by the second inspector with probability0.7. Assume that both inspectors inspect every item and thatif an item has no flaw, then neither inspector will detect aflaw.

a) Assume that the probability that an item has a flaw is0.10. If an item is passed by the first inspector, what isthe probability that it actually has a flaw?

b) Assume that the probability that an item has a flaw is0.10. If an item is passed by both inspectors, what is theprobability that it actually has a flaw?

Explanation / Answer

a) P(flaw)=0.10 P(inspector 1 detects a flaw ) = 0.90 P(flaw that is missed by inspector 1) = 0.1 P(flaw) * P(flaw that is missed by inspector 1) = 0.10 * 0.1=0.01 b) p(flaw that is missed by inspector 2) = 0.3 P(flaw) * P(flaw that is missed by inspector 1)*p(flaw that ismissed by inspector 2)= 0.1*0.1*0.3= 0.003 The second inspector is not so good in his job, but he makes nofalse positives and he lowers the change that some item is a flawthat is not detected with a great amount. This is due to the goodteamwork of the inspectors! Good Luck

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