Math Help - Probability of that system function

A system is made up of 3 components that operate independently from one another. For the system to function , atleast two components must function . We suppose that the probability of functioning of component no.1 is equal to 0.95, that of component no.2 is 0.9 and that of component no.3 is 0.8


i) What is the probability that the system functions?
ii) Given that the system functions , what is the probability that exactly two components function?

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A system is made up of 3 components that operate independently from one another. For the system to function , atleast two components must function . We suppose that the probability of functioning of component no.1 is equal to 0.95, that of component no.2 is 0.9 and that of component no.3 is 0.8


i) What is the probability that the system functions?
ii) Given that the system functions , what is the probability that exactly two components function?

Call the components A, B and C.

i) Calculate Pr(A and B and C') + Pr(A and B' and C) + Pr(A' and B and C) + Pr(A and B and C).

ii) Calculate [Pr(A and B and C') + Pr(A and B' and C) + Pr(A' and B and C)]/[Answer to (i)].