Question

The board of directors of a company knows that the probability that the carbon emission from the company’s manufacturing unit is exceeding the permissible level is 35%. A consultant is hired to use a carbon footprint calculator to test for the emission level. The accuracy of this test is said to be 85%.

What is the probability that the carbon emission from the manufacturing unit is within the permissible level, and the test predicts the same outcome?

A.) 0.2975
B.) 0.0525
C.) 0.0975
D.) 0.5525
E.) 0.6325

Answer 1

P(exceeding limit) = 0.35P(within limit)    = 1 - P(exceeding limit) = 0.65By conditional probability,P(within limit and test says within limit) = P(within limit) P(test says within limit | within limit) = P(within limit) (Accuracy) = (0.65)(0.85) = 0.5525Therefore, D.


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Answer 2

the company's production unit has a risk of carbon emission

the probability that the company is exceeding the permissible level is 35% =0.35

so there can only be two possibilities, either the company is exceeding the permissible level or its within the permissible level.

and the accuracy of the test that tests the emission level is 85%

so the probability that the carbon emission is within the permissible level is

1 - 0.35 = 0.65

probability that the test measures this accurately is 0.85

therefore when checking the probability that both events happen we have to multiply the 2 probabilities

the probability that carbon emission is within the permissible level and test predicts this outcome is - 0.65 x 0.85 = 0.5525

answer is D.0.5525