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toothpaste666
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Homework Statement
Suppose components A, B1 and B2 operate independently, in a system below, and the probabilities that anyone of the components will operate for 100 hours without failure are P(A) = 0.8,P(B1) = P(B2) = 0.9. The system works if A works and either B1 or B2 works. Find the probability that the entire system will operate without failure for 100 hours.
The Attempt at a Solution
the probability that the system runs for 100 hours without failure is equal to
P(A) and (P(B1) or P(B2))
for any events P(A) or P(B) = P(A) + P(B) - P(A and B)
so P(B1) or P(B2) = P(B1) + P(B2) - P(B1 and B2)
since B1 and B2 are independent events, P(B1 and B2) = P(B1)P(B2)
so P(B1) or P(B2) = P(B1) + P(B2) - P(B1)P(B2) = .9 + .9 - (.9)(.9) = .99
so the probability that the system runs without failure for 100 hours is
P(A) and (.99)
since both of these are independent events
P(A) and (.99) = P(A)(.99) = (.8)(.99) = .792
is this correct?