Answer:
The probability that carbon emissions from the factory are actually within the permissible level is 0.9132
Step-by-step explanation:
-let x represent when the emissions exceed the permissible level
-let y represent when the emissions does not exceed the permissible level
-let p represent when the test indicate that the factory's carbon emissions exceed the permissible level
-let q represent when the test indicate that the factory's carbon emissions does not exceed the permissible level
Probability that the the factory's carbon emissions exceed the permissible level and the test indicates that the factory's carbon emissions are not within the permissible level P(xq) =0.35*0.15= 0.0525
Probability that the factory's carbon emissions does not exceed the permissible level and the test indicates that the factory's carbon emissions are within the permissible level P(yp) = (1-.35)*0.85=0.65*0.85= 0.5525
the probability that carbon emissions from the factory are actually within the permissible level = 0.5525/(0.5525 + 0.0525) = 0.9132