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Help me in doing this problem Two components A and B are connected in parallel.

ID: 3218604 • Letter: H

Question

Help me in doing this problem

Two components A and B are connected in parallel. The lifetime of A is exponentially distributed with a mean of 30 hours. The lifetime of B is exponentially distributed with a mean of 40 hours. What is the probability that at least one of the components survives for 50 hours. If the components are connected in series, what is the probability that the system survives 50 hours, that is both components survive 50 hours. Write the PDF of the time at which this system fails.

Explanation / Answer

a) probabilty that at least one of the system works =1-P(both of the system fails till 50 hours)

=1-((1-e-50/30)*(1-e-40/30)) =1-(0.5973) =0.4027

b)probabilty that both component survives =e-50/30*e-40/30 =0.0498

probabilty that system will fail=1-P(both of the system works) =1-(e-t/30*e-t/40) =1-e-7t/120