the board of directors of a company knows that the probability that the carbon emission from the companys…

the board of directors of a company knows that the probability that the carbon emission from the companys 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%. select the correct answer. 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

the board of directors of a company knows that the probability that the carbon emission from the companys 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%. select the correct answer. 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

Answer:

D. 0.5525

Explanation:

Step1: Calculate probability of emission within limit

The probability that the carbon - emission is exceeding the permissible level is $P(\text{exceed}) = 0.35$. So the probability that the carbon - emission is within the permissible level is $P(\text{within})=1 - 0.35=0.65$.

Step2: Calculate probability of correct prediction

The accuracy of the test is 85% or 0.85. We want the probability that the emission is within the limit and the test predicts it correctly. Since the test correctly predicts 85% of the cases, the probability that the emission is within the limit and the test predicts it correctly is $P = 0.65\times0.85$.

Step3: Perform multiplication

$0.65\times0.85 = 0.5525$.