Fasteners used in aircraft manufacturing are slightlycrimped so that they lock enough to avoid looseningduring vibration. Suppose that 95% of all fasteners passan initial inspection. Of the 5% that fail, 20% are soseriously defective that they must be scrapped. Theremaining fasteners are sent to a recrimping operation,where 40% cannot be salvaged and are discarded. Theother 60% of these fasteners are corrected by therecrimping process and subsequently pass inspection.a. What is the probability that a randomly selectedincoming fastener will pass inspection either initiallyor after recrimping?b. Given that a fastener passed inspection, what is theprobability that it passed the initial inspection anddid not need recrimping?
Fasteners used in aircraft manufacturing are slightly
crimped so that they lock enough to avoid loosening
during vibration. Suppose that 95% of all fasteners pass
an initial inspection. Of the 5% that fail, 20% are so
seriously defective that they must be scrapped. The
remaining fasteners are sent to a recrimping operation,
where 40% cannot be salvaged and are discarded. The
other 60% of these fasteners are corrected by the
recrimping process and subsequently pass inspection.
a. What is the probability that a randomly selected
incoming fastener will pass inspection either initially
or after recrimping?
b. Given that a fastener passed inspection, what is the
probability that it passed the initial inspection and
did not need recrimping?
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