SOLUTION: a system of 5 identical units consists of two parts A and B which are connected in series.part A has 2 units connected in parallel and part B has 3 units connected in parallel.all

Question 905772: a system of 5 identical units consists of two parts A and B which are connected in series.part A has 2 units connected in parallel and part B has 3 units connected in parallel.all the units function independently with probability of failure 1/2.then the reliability of the system is
a)31/32
b)11/32
c)1/32
d)21/32
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have 2 parts.
they are connected in series.
any failure in part A or part B will stop the system.
within part A you have 2 units in parallel.
for part A to fail both units would have to fail.
within part B you have 3 units in parallel.
for part B to fail all 3 units would have to fail.
your probabilities of failure are:

for part A, 1/2 * 1/2 = 1/4 probability that all 2 units will fail at the same time.

for part B, 1/2 * 1/2 * 1/2 = 1/8 probability that all 3 units will fail at the same time.

the probability that part A will fail is 1/4 and the probability that part B will fail is 1/8.

the probability that part A will fail or part B will fail is equal to p(A) + p(B) - p(AB)

that's the probability that A will fail plus the probability that B will fail minus the probability that both A and B will fail at the same time.

you get probability of system failure = (1/4) + (1/8) - (1/4) * (1/8)

convert evrything to a denominator of 32 andyou get:

p(A) + p(B) - p(AB) = 8/32 + 4/32 - 1/32 which becomes 12/32 - 1/32 = 11/32.

the probability that the system will fail completely is 11/32.

the reliability of the system is 1 minus the probability that the system will fail which is equal to 32/32 - 11/32 = 21/32.

that looks like selection d.

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