Help please!!!!
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?

Some one said 0.2% but I can't fiqure out how they got that answer. Steps would be nice.

Question

Help please!!!!
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?

Some one said 0.2% but I can't fiqure out how they got that answer. Steps would be nice.

kitkat16 · Answer

P= 0.05 * 0.08 = 0.004 = 0.4% 
So they would both fail
yes no ???? anyone :(

kitkat16 · Answer

I hate math :(

kitkat16 · Answer

@ganeshie8 check please!!!

kitkat16 · Answer

@Preetha can you check my work please

ganeshie8 · Answer

If the gears on the machine are in no way linked to each other, what are the chances that both will fail?

ganeshie8 · Answer

that means the events are "independent"

ganeshie8 · Answer

for independent events, we have :

$\large  P(A \cap   B) =  P(A) \cdot P(B)   $

ganeshie8 · Answer

right ?

ganeshie8 · Answer

Probability for both failing =   $0.05 *  0.08 = 0.004 = 0.4\% $

kitkat16 · Answer

yes. thank you!!!!

ganeshie8 · Answer

np :)