Question

A company manufactures kitchen chairs at one of three facilities. Twenty-five percent of the chairs are manufactured at facility A, 30 percent at facility B, and 45 percent at facility C. Of those chairs manufactured at facility A, 25 percent have pads, at facility B, 15 percent, and at facility C, 10 percent. Suppose a kitchen chair made by this company is selected at random. (a) Find the probability the chair was manufactured at facility C and has pads. (b) Find the probability the chair has pads. (c) Suppose the chair selected has pads. Find the probability it was manufactured at facility B.

Answer 1

P(facility A) = 0.25

P(facility B) = 0.30

P(facility C) = 0.45

P(pads | facility A) = 0.25

P(pads | facility B) = 0.15

P(pads | facility C) = 0.10

a) P(facility C and has pads) = P(pads | facility C) * P(facility C) = 0.1 * 0.45 = 0.045

b) P(chair has pads) = P(pads | facility A) * P(facility A) + P(pads | facility B) * P(facility B) + P(pads | facility C) * P(facility C)

                                 = 0.25 * 0.25 + 0.15 * 0.3 + 0.1 * 0.45

                                 = 0.1525

c) P(facility B | pads) = P(pads | facility B) * P(facility B) / P(chair has pads)

                                  = 0.15 * 0.3 / 0.1525

                                  = 0.2951