In a certain assembly plant, three machines b1, b2, and b3, make 35%, 40%, and 25%, respectively. it is known from past experience that 2%, 3%, and 4% of the products made by each machine, respectively, are defective. a finished product is randomly selected and found to be defective, what is the probability that it was made by machine b3? enter your answer as a decimal and use 3 significant digits.

I suppose the part about

"B1, B2, and B3, make 35%, 40%, and 25%"

should be taken to mean produces 35% of some product, produces 40%, and produces 25%. Then

Each machine has some probability of making a defective product - denote this event by . Then

We want to find the probability that a defective product was made by machine , i.e. . By definition of conditional probability and the law of total probability, we have

(def. of conditional probability)

(def. of conditional probability)

(law of total probability)

(def. of conditional probability; this result is also known as Bayes' theorem)

So we have

d

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