The Acme Machine Shop has five machines that periodically break down and require service.The average time between breakdowns is 4 days, distributed according to an exponential distribution.The average time to repair a machine is 1 day, distributed according to an exponentialdistribution. One mechanic repairs the machines in the order in which they break down. Determine the probability that the mechanic is idle.

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The Acme Machine Shop has five machines that periodically break down and require service.
The average time between breakdowns is 4 days, distributed according to an exponential distribution.
The average time to repair a machine is 1 day, distributed according to an exponential
distribution. One mechanic repairs the machines in the order in which they break down. Determine the probability that the mechanic is idle.

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