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A sensory device consisting of two identical sensors that are connected in series will fail if any one of the two (or both) sensors fails.

A sensory device consisting of two identical sensors that are connected in series will fail if any one of the two (or both) sensors fails. Assume that the lifetime of each sensor is according to the Exponential distribution with an average lifetime of 5 years, and that each sensor's lifetime is independent of the other.

What is the probability that the device consisting of the two sensors that are connected in series will last for at least 5 years?

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