Determine fraction of time that no light bulbs are working, Other Subject

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Determine fraction of time that no light bulbs are working

Problem

My home uses two light bulbs. On average, a light bulb lasts for 100 days (exponentially distributed). When a light bulb burns out, it takes an average of 10 days (exponentially distributed) before I replace the bulb.

1. Formulate a three-state birth-death model of this situation.

2. Determine the fraction of the time that both light bulbs are working.

3. Determine the fraction of the time that no light bulbs are working.

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