Suppose that each engine can be inspected before theflight. After inspection, each engine is labeled as being ineither good or bad condition. You are given thatP(inspection says engine is in good condition | engine willfail) .001P(inspection says engine is in bad condition | engine willfail) .999P(inspection says engine is in good condition | engine willnot fail) .995 P(inspection says engine is in bad condition | engine willnot fail) .005 a If the inspection indicates the engine is in bad con-dition, what is the probability that the engine will fail on the flight?b If an inspector randomly inspects an engine (that is,with probability .001 she chooses an engine that is aboutto fail, and with probability .999 she chooses an enginethat is not about to fail), what is the probability that shewill make an error in her evaluation of the engine?
Suppose that each engine can be inspected before the
flight. After inspection, each engine is labeled as being in
either good or bad condition. You are given that
P(inspection says engine is in good condition | engine will
fail) .001
P(inspection says engine is in bad condition | engine will
fail) .999
P(inspection says engine is in good condition | engine will
not fail) .995
P(inspection says engine is in bad condition | engine will
not fail) .005
a If the inspection indicates the engine is in bad con-
dition, what is the probability that the engine will fail on
the flight?
b If an inspector randomly inspects an engine (that is,
with probability .001 she chooses an engine that is about
to fail, and with probability .999 she chooses an engine
that is not about to fail), what is the probability that she
will make an error in her evaluation of the engine?
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