Question

4000 points A toreman tor an injechan-molding hrm admits that nnt his shits, he togets to shut ott the injection machine on hs line Ihis causes the machine to nverhest, increasing the probahility that a detective molding will he produced during the eany morning run from 1% to 19% Let F forgels lo shul off the injeclion machine and D-defettive. se a prohahility tree 1o ansrthe tolkwing questions In aur decamais 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

Define events
1. F = event of forgetting to shut off machine.
2. D = event of product being defective.

P(F and D) = 0.09*0.19 = 0.0171
P(F and ~D) = 0.09*(1-0.19)=0.0729
P(~F and D) = (1-0.09)*0.01= 0.0091
P(~F and ~D) = (1-0.09)*(1-0.01)=0.9009

a)
P(D) = [P(F and D)+P(~F and D)]
= 0.0171 + 0.9009
= 0.918

b)
By definition of conditional probability
P(F|D)=P(F and D)/P(D)
=P(F and D)/ P(D)
= 0.0171/0.918
= 0.018627