The board of directors of a company knows that the probability that carbon emissions from the company’s factory exceed the permissible level is 45%. They hire a consultant who uses a carbon footprint calculator to test the emissions level. The test, which has an accuracy rate of 85%, indicates that the factory's carbon emissions are within the permissible level.

Given the test result, the probability that carbon emissions from the factory are actually within the permissible level is.
-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)
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)
the probability that carbon emissions from the factory are actually within the permissible level is
P= P(yp) / (P(yp) +P(xq))