Question

A foreman for an injection-molding firm admits that on 18% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 10% to 28%.

Let F = forgets to shut off the injection machine and D = defective.

Use a probability tree to answer the following questions:

(Round all answers to four decimals)

a) What’s the probability a molding from the early morning run is defective?

b) The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?

Answer 1

R = forget to shut off

D = Defective moulding

S= Shutting off machine

P(R) = 0.18

P(D|R) = 0.28

P(S) = 1-0.18 = 0.82

P(S|D) = 0.1

P(D)

= P(R) P(D|R) + P(S) P(S|D)

= 0.18* 0.28 + 0.82*0.1

= 0. 1324

b)

P(R|D) = P(R and D) / P(D)

= P(R) P(D|R) / P(D)

= 0.18 * 0.28/0.1324

= 0.380664