please show all the work, and use tree diagram if possible. 92. Fasteners used i

Question

please show all the work, and use tree diagram if possible.

92. 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 sal- vaged 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?

Explanation / Answer

probabilty that randomely selected fastener will pass insopection inititally or after recrimping

=P(it passed initially+falied in first test*sent for crimping and passed) =0.95+0.05*0.8*0.6=0.974

b)probabilty that it passed in intitial inspection given it passed inspection =P(passed initially)/P(passed inspection)

=0.95/0.974=0.9754

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