SOLUTION: Solve the below Bayes' theorem question QNo3=A manufacturer of a firm claims that 70% of its new hires turn out to be good workers and the rest are to be poor workers. The comp

Algebra ->  Probability-and-statistics -> SOLUTION: Solve the below Bayes' theorem question QNo3=A manufacturer of a firm claims that 70% of its new hires turn out to be good workers and the rest are to be poor workers. The comp      Log On


   

Question 1197352: Solve the below Bayes' theorem question
QNo3=A manufacturer of a firm claims that 70% of its new hires turn out to be good workers and the rest are to be poor workers. The company advised their current to qualify a reasoning test. Eighty percent of the good workers and forty percent of the poor workers pass the reasoning test. If the company makes the reasoning test be a part of its hiring procedure, what then is the probability of the new hires that,
1. will turn out to be good workers?
ii. will turn out to be poor workers?
iii. Depict the turn out percentage of the workers on the Bayes' tree diagram
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
iii. Depict the turn out percentage of the workers on the Bayes' tree diagram
The Baye's tree diagram:



Notice that we multiply the probabilities along each of the 4 paths
to the far right.

Notice that the sum of the probabilities at the end all add up to 1,
That is, 0.56 + 0.14 + 0.12 + 0.18 = 1.00 = 100%
what then is the probability of the new hires that,
1.i. will turn out to be good workers?
Notice that the potentially GOOD workers produced the 0.56 and the 0.14,
so we add those and get 0.56 + 0.14 = 0.70 = 70%
ii. will turn out to be poor workers?
Notice that the potentially POOR workers produced the 0.12 and the 0.18,
so we add those and get 0.12 + 0.18 = 0.30 = 30%

Edwin