A system can have three different types of defects: A1, A2, A3. We are given the following probabilities.
P(A1) = .12 P(A2) = .07 P(A3) = .05 P(A1 U A2) = .13 P(A1 U A3) = .14 P(A2 U A3) = .10 P(A1 and A2 and A3) = .01
What is the probability that the system has both type 1 and type 2 defects, but not a type 3 defect.
I'm confusing the heck out of myself with this one. I've drawn out a Venn Diagram to try and help visualize what we want, A1 and A2 are the left and right circles, A3 is the bottom circle. We are looking for A1, A2, and everything not A3 to be shaded. So we need to do the following:
P(A1) + P(A2) + P(A3') - P(A1 U A2) - P(A1 U A3)- P(A2 and A3) = + P(A1 and A2 and A3) .12 + .07 + .05 - .13 - .14 - .10 + .01 = -.12
-.12 is clearly not right. Can someone please shed some light on this for me?
Update: Can we do something like 1 - P(A3)? This would give us everything excluding A3.
If you are going to down vote the question, at least provide some feedback so I can improve the question.