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?

Question

mathmate · Answer

Since both gears are "expired", so the respective probabilities of failure are
5% for one, and 8% for the other.
The probability of both independent events succeeding (i.e. failing) is the product of their probabilities.

anonymous · Answer

They are both expired so the older they get the more they will fail.