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HMMT 2002 V7

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A manufacturer of airplane parts makes a certain engine that has a probability pp of failing on any given flight. Their are two planes that can be made with this sort of engine, one that has 3 engines and one that has 5. A plane crashes if more than half its engines fail. For what values of pp do the two plane models have the same probability of crashing?

Dataset text NuminaMath olympiads. Quoted with source.

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0, \frac{1}{2}, 1

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