# Probability : k-out-of-n System

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Consider the k-out-of-n system (explanation: a system consists of n independent components. Each component functions with probability p. The system as a whole functions if at least k components are functioning (1 <= k <= n)). Suppose we visit this system at time t=3 and replace all failed components, at a cost of $75 each. If the system has failed, it costs us an additional $1000. Compute the expected total cost incurred at time 3.

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##### Solution Summary

A probability involving a k-out-of-n system is solved.

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Probability that system fails = nCk * p^k * ...

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