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

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: