A machine needs 2 of its gears replaced. You find 2 gears, one manufactured 5 years ago and the other manufactured 10 years ago. The specifications sheet says that the chance of failure is 5% after 5 years and increases to 8% after 10 years. If the gears on the machine are in no way linked to each other, what are the chances that both will fail?

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5 April, 15:16

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Kieran Larson · Answer 1

These are independent events so

P (A and B) = P (A) * P (B)

Therefore

P (Both gears fail) = 0.05 * 0.08 = 0.004 or 0.4%