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

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%