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

(There are no options, you have to put the answer in the box).

Answer 1

The probability that the emissions are within the permissible level but the test incorrectly indicates they are not is 9.75%.

Step-by-step explanation:

The question is asking about the probability that the carbon emissions from the factory are within permissible level, yet the test incorrectly indicates they are not. To find this, we'll need to consider two probabilities:

• The probability that the emissions are within the permissible level.
• The probability that the test inaccurately predicts that the emissions exceed the permissible level.

Given that the probability of emissions exceeding the permissible level is 35%, the complementary probability that they are within the permissible level is 100% - 35% = 65%.

The accuracy of the test is 85%, which means that the test incorrectly predicts the outcome 15% of the time (100% - 85%).

To find the probability that the emissions are within the permissible level and the test predicts the opposite, we multiply these two probabilities:

Probability = 65% * 15% = 0.65 * 0.15 = 0.0975 or 9.75%

Therefore, there is a 9.75% chance that the emissions are within the permissible level and the test incorrectly indicates that they are not.