Hi !

I'm very unsure of my answers to this problem :

A company produces boxes. 1% of the boxes have a defect. A control of the boxes detects and eliminates 95% of the defective boxes but eliminates by mistake 2% of the boxes produced.

1) What's the probability not to eliminate a box, knowing it is not defective ?

2) What's the probability the control doesn't work, i.e. that a non defective box is eliminated or a defective box is accepted ?

3) What's the probability an accepted box is defective ?

P(D) = 0,01

P(E\D) = 0,95

P(E n nonD) = 0,02

1) P(nonE/nonD)=1-P(E/nonD)=1-0,02 = 0,98

2) Pcontrol-failure = P(E n nonD)+P(nonE n D) - P(E n nonD) n (nonE n D) = p(D)*p(E/D) + p(nonD)*p(E/nonD)- P(E n nonD) n (nonE n D)

Here I am stuck. I calculated that p(D)*p(E/D) + p(nonD)*p(E/nonD) = 0,0203. But for me the part I put in bold are exclusive events. However, I must be wrong because I was given 0,0195 as an answer.

Are those events independant or exclusive ? I can't wrap my mind around this even though it's so basic I'm sorry...

3) P(D/nonE) = P(nonE/D).P(D)/P(nonE)=(1- P(E/D)).P(D) / P(nonE)

With P(nonE)= P(nonE/D).P(D) + P(nonE/nonD).P(nonD) = (1-P(E/D)).P(D) + P(nonE/nonD).P(nonD)

Thank you for your help !!