Question

A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 20%, 25%, and 55%, respectively, of all jobs bid on by the company. For i-1, 2, 3, define Ei to be the event that a job is estimated by engineer i. The following probabilities describe the rates at which the engineers make serious errors in estimating costs: P(errorlE1) -0.02, P (errorlE2) -0.03, and P(errorlE3) -0.0 Complete parts a through d.

If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 1? PE, error) | | (Round to the nearest thousandth as needed.)

Answer 1

To find the probability that the error was made by engineer 1, we can use Bayes' theorem.

Step-by-step explanation:

To find the probability that the error was made by engineer 1, we need to use Bayes' theorem. Let A be the event that the error was made by engineer 1, and B be the event that a serious error occurred. We need to find P(A|B), which is the probability of A given B.

According to Bayes' theorem, P(A|B) = P(B|A) * P(A) / P(B). We are given P(error|E1) = P(B|A) = 0.02, P(E1) = P(A) = 0.20, and P(B) = 0.20*0.02 + 0.25*0.03 + 0.55*0.0.

Plugging these values into the formula, we get P(A|B) = (0.02 * 0.20) / (0.20*0.02 + 0.25*0.03 + 0.55*0.0) = 0.065.