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a kind of tire has a 80% probability of exploding after 20000 miles. What is the probability that a set of 4 tires will last longer that 20000 miles without any of tham exploding?

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Probability of one tire NOT exploding = 1-80%=0.2
Probability of ALL FOUR tires NOT exploding = 0.2^4 = 0.0016

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