Question 1018149: A biomedical research company produces 49% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 1.1% of the insulin produced at the plant in Kansas City is defective, while 0.65% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Make a table, which makes it easier. Use large numbers to limit decimals
place=====good======defective===total
JC========9935========65=======10000
KC========9890=======110=======10000
BUT, they aren't equal, so I will increase to 100,000 and make JC 51000
=========50668.5=====331.5=====51000; multiplying the above cells by 5.1
=========48461=======539=======49000; multiplying the above b 4.9
=========98129.5=====870.5====100000
Given that the part is defective (870.5 out of 100000), the probability it came from JC is 331.5/870.5=0.3808
Intuitively it is a little more likely because a little more is made there; however, it is less than 2/3s as likely on a per unit basis, so the probability should be less than half.
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