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A string of holiday lights contains 15 lights. The lights are wired in series, so that if any light fails then the whole string will go dark. Each light has probability 0.05 of failing during a three-year period. The lights fail independently of each other.
What is the probability that the string of lights will go dark within a three-year period? That is, what is the probability that at least one light in the string will fail within three years?
Express your answer in decimal form to 3 decimal places.
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