SOLUTION: This question is really confusing me, not quite sure where to start. A foreman for an injection-molding firm admits that on 39% of his shifts, he forgets to shut off the injecti

Question 997079: This question is really confusing me, not quite sure where to start.
A foreman for an injection-molding firm admits that on 39% 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 4% to 15%. 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?
Probability = ?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Given:
A foreman forgets to shut off machine 39% of the time.
If he forgets, 15% of moulds are defective.
If he does not, 4% of moulds are defective.
Given that a mould is defective, find probability that he forgot to turn off machine the night before.

Solution:

Define events
1. F = event of forgetting to shut off machine.
2. D = event of product being defective.
P(F and D) = 0.39*0.15=0.0585
P(F and ~D) = 0.39*(1-0.15)=0.3315
P(~F and D) = (1-0.39)*0.04=0.0244
P(~F and ~D) = (1-0.39)*(1-0.04)=0.5856

By definition of conditional probability
P(F|D)=P(F and D)/P(D)
=P(F and D)/[P(F and D)+P(~F and D)]
=0.0585/(0.0585+0.0244)
=0.706 (approx.)

Answer:
The probability that the foreman forgot to shut the machine is 0.706, given that the product was defective.
RELATED QUESTIONS
A foreman for an injection-molding firm admits that on 10% of his shifts, he forgets to... (answered by Theo)

A foreman for an injection-molding firm admits that on 10% of his shifts, he forgets to... (answered by ikleyn)

I know that this doesn't go in this section of questions, but there wasn't a sectioin for (answered by Earlsdon)

This question is more on rational equations,Im not really quite sure where to begin.... (answered by josgarithmetic)

pleae help me. this is o confusing and i am not sure where to start. Has to be wriiiten... (answered by DrBeeee)

Let f(x)=2x+3 and g(x)=x^2 Determine the formula for the following composition: (g (answered by Fombitz)

These kind of problems are really confusing to me... simplify 5cis115degrees *... (answered by jim_thompson5910)

This question is really throwing me off, I'm not even sure how to start it off..Can... (answered by rothauserc)

I am not quite sure where this falls into but here is the question. rearrange... (answered by lynnlo)