Expert: Abe Mantell - 1/14/2011

Question
At an electronics plant ,It is known from past experience that the probability is .90 that a new worker who has attended the company training program will meet production quota and the corresponding probability is .30 for a new worker who has not attended the company training program. if 75% of all new workers attend the training program, what is the probability that a new worker will meet production quota?

Answer
Hello Abhay,

We can express the information as:
M=worker has met production quota
T=worker attended training
P(M|T)=0.9, P(M|T')=0.3
P(T)=0.75, thus P(T')=0.25
and we want to find P(M)

Using the law of total probability, we get
P(M)=P(M and T) + P(M and T')
= P(T)P(M|T) + P(T')P(M|T')
= 0.75*0.9 + 0.25*0.3
= 0.675 + 0.075
= 0.75

OK?

Abe