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 in % form.
If someone could show me the steps I would really appreciate it! Thanks!!!

Answer 1

Probability that gear 1 will fail = 5/100 (upto 10 years) 
and 8/100 (after 10 years)

Probability that both will fail = 5/100 * 8/100
= 40/10000
= 0.4 %