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?

A. 0.2%
B. 0.9%
C. 40%
D. 7.5%
E. 0.4%

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?

A. 0.2%
B. 0.9%
C. 40%
D. 7.5% 
E. 0.4%

anonymous · Answer

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. 
 -----------------------------
 P(both fail) = 0.05*0.08 = 0.004 = 0.4%

justdoublechecking · Answer

That's what I thought! Thank you!

anonymous · Answer

i did it myself, i got the same answer. you both are correct.

justdoublechecking · Answer

Thank you too! :D