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 manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this? 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 manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this? a. 0.2975 b. 0.0525 c. 0.0975 d. 0.5525 e. 0.6325

Answer

Explanation:

Step1: Identify relevant probabilities

Let $P(E)$ be the probability that the carbon - emission exceeds the limit. Here $P(E)=0.35$. Let the accuracy of the test be $P(T|E)$ (probability that the test is positive given that the emission exceeds the limit), and the accuracy of the test is $85%$ or $0.85$.

Step2: Use the formula for joint probability

The probability that the manufacturing unit has carbon - emission beyond the permissible level and the test predicts this is given by the formula for joint probability $P(E\cap T)=P(T|E)\times P(E)$. Substitute $P(T|E) = 0.85$ and $P(E)=0.35$ into the formula: $P(E\cap T)=0.85\times0.35$ $P(E\cap T)=0.2975$

Answer:

A. $0.2975$