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Omni-MATH / A manufacturer of airplane parts makes a certain engine that has a probability…

Problem

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problem

A manufacturer of airplane parts makes a certain engine that has a probability pp of failing on any given flight. There 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?
Plain-text mathematical notation (without MathML)
A manufacturer of airplane parts makes a certain engine that has a probability p of failing on any given flight. There 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 p do the two plane models have the same probability of crashing?
Original LaTeX notation
A manufacturer of airplane parts makes a certain engine that has a probability $p$ of failing on any given flight. There 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 $p$ do the two plane models have the same probability of crashing?

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Source and history

task_id
b0dd9b66-f5a8-5147-804c-3c2d1d0e21a7
task_key
test--b0dd9b66-f5a8-5147-804c-3c2d1d0e21a7
task_revision_id
1
config / split
/ test

Official source

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