A system is made up of three components placed in parallel that operate simultan

Question

A system is made up of three components placed in parallel that operate simultaneously. The probability that component no. 1 functions is equal to 0.9. In the case of component no. 2, this probability is equalt to 0.95 if component no. 1 functions, and to 0.8 otherwise. Finally, the probability that component no. 3 functions is equalt to 0.99 if components nos. 1 and 2 function, to 0.75 if components nos. 1 and 2 do not function, and to 0.8 otherwise. Calculate the probability that the system functions. Given that the system functions, what is the probability that component no. 2 functions? Calculate the probability that component no. 3 functions.

Explanation / Answer

Do all three components need to function in order for the system to function?

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