SHOW WORK (MASTERY Problem) Chapter 3 Review Practice Problems, Problem 26: An i

Question

SHOW WORK

(MASTERY Problem) Chapter 3 Review Practice Problems, Problem 26: An industry uses three methods M1, M2, and M3 to train their workers. Of all the workers trained, 50% are trained by method M1, 28% by method M2, and the rest, 22%, by method M3. Further 10% of those trained by method M1 do not perform their job well (A), while 5% trained by method M2 and 15% by methods M3 also do not perform their job well. A randomly selected worker does not perform his job well. Find the probability that the worker was trained by (a) method M1, (b) method M2, and (c) method M3 First, what is the marginal probability of an employee not doing his or her job well, P(A) Now, what are the requested conditional probabilities? (a) P(MI | A)= (b) P(M21A)= (c) P(M3 | A) =

Explanation / Answer

P(M1)=0.5

P(M2)=0.28

P(M3)=0.22

P(A|M1)=0.1

P(A|M2)=0.05

P(A|M3)=0.15

Thus P(A)=P(A|M1)*P(M1)+P(A|M2)*P(M2)+P(A|M3)*P(M3)=0.1*0.5+0.05*0.28+0.15*0.22=0.097

a) P(M1|A)=P(A|M1)*P(M1)=0.1*0.5/0.097=0.5155

b) P(M2|A)=P(A|M2)*P(M2)=0.05*0.28/0.097=0.1443

c) P(M3|A)=P(A|M3)*P(M3)=0.15*0.22/0.097=0.3402

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