Question: Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose

Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995.
The success or failure of a bulb is independent of the success or failure of other bulbs.
(a) What is the probability that in a string of 100 lights all 100 will last 2 years?
(b) What is the probability that at least one bulb will burn out in 2 years?

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