The board of directors of a company knows that the probability that carbon emissions from the company’s factory exceed the permissible level is 35%. They hire a consultant who uses a carbon footprint calculator to test the emissions level. The accuracy of the test is 85%.
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is

Question

The board of directors of a company knows that the probability that carbon emissions from the company’s factory exceed the permissible level is 35%. They hire a consultant who uses a carbon footprint calculator to test the emissions level. The accuracy of the test is 85%.
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is

boldjon · Answer

i think we can do this if we do not get lost
my method is to forget about working with the decimals and picking some actual number to start with, say they have 10,000 trials, of which 35% or 3500 exceed the level

boldjon · Answer

ou test with 85% accuracy so of the 3500 that are bad, 85% of the, or .85×3500=2979 test correctly as bad, whereas 15% of the remaining 6500 also test bad, or .15∗6500=975 test bad

anonymous · Answer

so the answer is 975?

boldjon · Answer

the total number that test bad are 2979+975=3957 and the total that are actually bad are 2979 so your probability is

boldjon · Answer

2979/3957