(Answered) Question the light used in the operation theater of a

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Question: The light used in the operation theater of a hospital has two bulbs. One bulb is sufficient to get the necessary lighting. The bulbs are connected in such a way that when one fails, automatically the other gets switched on. The life of each bulb is exponentially distributed with a mean of 5000 hours and the lives of the bulbs are independent of one another. What is the probability that the combined life of the light is greater than 7000 hours?

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