2.A company manufactures car batteries at three plants. Plant A produces 850 batteries a day, Plant B produces 630 batteries a day, Plant C produces 520 batteries a day. Experience indicates that 4% of the batteries produced at plant A are defective, 5% of the batteries in plant B are defective, and 2% of the batteries in Plant C are defective. Each day, all batteries produced are shipped to the company’s warehouse. Suppose that a battery randomly selected in the warehouse is found defective, what is the probability that it was produced at ( a) plant A ( b ) Plant B ( c ) Plant C.

Solution:

(a)

850*4%/(850*4%+630*5%+520*2%)= 0.448

So the probability that it was produced at A is 0.448

(b)

630*5%/(850*4%+630*5%+520*2%)= 0.415

So the probability that it was produced at B is 0.415

(c)

520*2%/(850*4%+630*5%+520*2%)= 0.137

So the probability that it was produced at C is 0.137