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Consider the system comprised of three components as shown below. Suppose • The lifetime of Component...

Consider the system comprised of three components as shown below. Suppose • The lifetime of Component 1 is exponentially-distributed with parameter λ1 = 1/10. • The lifetime of Component 2 is exponentially-distributed with parameter λ2 = 1/20. • The lifetime of Component 3 is exponentially-distributed with parameter λ3 = 1/15. The system is working if both (A) Component 1 is working, and (B) Component 2 or/and Component 3 is working. Compute the probability that the system is still working at time t = 8.

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