SOLUTION: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is .02. What is the probabil

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Question 258832: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

Found 2 solutions by Fombitz, richwmiller:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
THANKS TO RICHWMILLER for pointing out the error in the failure rate value and putting in the correction: I'm not sure I'd fly in a plane with a 0.2 failure rate for the alternator.
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P(both fail)=%280.2%29%280.2%29=0.04
P(neither fail)=%280.8%29%280.8%29=0.64
P(one fails)=P(first fails,second doesn't)+P(first doesn't, second fails)=%280.2%29%280.8%29%2B%280.8%29%280.2%29=0.32
Ptotal=0.04%2B0.64%2B0.32=1 (all possible events are covered)

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Fombitz did some good calculating but read the data incorrectly.
It is .02 not .2
P(both fail)=%280.2%29%280.2%29=0.04
P(neither fail)=%280.8%29%280.8%29=0.64
P(one fails)=P(first fails,second doesn't)+P(first doesn't, second fails)=%280.2%29%280.8%29%2B%280.8%29%280.2%29=0.32
Ptotal=0.04%2B0.64%2B0.32=1 (all possible events are covered
Adjusting the work then
P(both fail)=%280.02%29%280.02%29=0.0004 2/100*2/100=4/10000
P(neither fail)=%280.98%29%280.98%29=0.9604
P(one fails)=P(first fails,second doesn't)+P(first doesn't, second fails)=%280.02%29%280.98%29%2B%280.98%29%280.02%29=0.0392
If the first doesn't fail how are you going to know if the second one did failed?
Ptotal=0.0004%2B0.9604%2B0.0392=1 (all possible events are covered