A communications system consists of n components, each of which will, independently, function with probability p. The

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A communications system consists of n components, each of which will, independently, function with probability p. The total system will be able to operate effectively if at least one-half of its components function.

(a) For what values of p is a 5-component system more likely to operate effectively than a 3-component system?

(b) In general, when is a 2k + 1 component system better than a 2k − 1 component system?

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