Question

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. If the gears on the machine are not linked to each other, the probability that both replacement gears will fail is 0.2 0.4 0.9 7.5 40 %.

Answer 1

your answer would be 0.4 percent. option B for plato :)
#PLATOlivesmatter #PLATOfam

Answer 2

Option 2 - 0.4%

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,

`\text{P(both fail)} = 5\%* 8\%`

`\text{P(both fail)} = 0.05* 0.08`

`\text{P(both fail)} = 0.004`

`\text{P(both fail)} = 0.4\%`

Therefore, Option 2 is correct.