Question 1159301: Four machines are in operation. Machine 1 produces five percent defective items,
machine 2 three percent, machine 3 four percent, and machine 4 eight percent. A machine
is selected at random and an item picked.
a. Given that the item is defective, find the probability that it came from machine 2.
b. Given that the item is defective, find the probability that it didn’t come from machine 2.
c. Given that the item is not defective, what is the probability that it is from machine 2?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Look at 1000 from each machine
====Def======ND===Total
1-----50 ----- 950---- 1000
2---- 30---------970-----1000
3-----40--------960----1000
4-----80--------920----1000
tot--200--------3800---4000
If defective (200) probability it came from machine 2 is 30/200 or 0.15
The probability it did not come from machine 2 is 0.85, the complement
If it is not defective (3800) the probability it was from machine 2 is 970/3800 or 0.255.
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