Question: The time until the light in Bobs office fails is exponentially distributed with mean 2 hours. The time until the computer crashes in Bobs office

The time until the light in Bob’s office fails is exponentially distributed with mean 2 hours. The time until the computer crashes in Bob’s office is exponentially distributed with mean 3 hours. Failure and crash times are independent.
(a) Find the probability that neither the light nor computer fail in the next 2 hours.
(b) Find the probability that the computer crashes at least 1 hour after the light fails.

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