Answer:
Option 2 - 0.4%
Step-by-step explanation:
Given : A machine needs two of its gears replaced. You find two gears, one manufactured 5 years ago and the other manufactured 10 years ago. The specification sheet says that the chance of gear failure is 5% after 5 years and increases to 8% after 10 years.
To find : If the gears on the machine are not linked to each other, the probability that both replacement gears will fail?
Solution :
The specifications sheet says that the chance of failure is 5% after 5 years and increases to 8% after 10 years.
But, If the gears on the machine are in no way linked to each other
Then the chances that both will fail,
[tex]\text{P(both fail)} = 5\%\times 8\%[/tex]
[tex]\text{P(both fail)} = 0.05\times 0.08[/tex]
[tex]\text{P(both fail)} = 0.004[/tex]
[tex]\text{P(both fail)} = 0.4\%[/tex]
Therefore, Option 2 is correct.
