Answer to Question #49164 in Statistics and Probability for diana

Question

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?

Answer 1

A machine needs 2 of its gears replaced. You find 2 gears, one manufactured 5 years ago and the other manufactured 10 years ago. If p1 = 0.05 and p2 = 0.08 and the gears on the machine are in no way linked to each other, the chances that both will fail will be P = 0.05*0.08 = 0.004 or 0.4%