[jtr]

Hi, JKKK.

I didn't check this thread for a while and it seems BruceZ has answered your question very capably as always.

Just to let you know: I got my original answer of 0.05 using a very simple graphical method. You know what a Venn diagram is right?

1) If we draw a framing rectangle to denote the whole universe of possibilities, all the mutually exclusive outcomes (i.e., the area of the rectangle) must be 1.

2) We know that P(A) = 0.5 and P(B) = 0.35. We also know that A and B are not mutually exclusive. So we can draw two circles, one representing A with an area of 0.5, and one representing B with an area of 0.35. Plus they overlap a bit. (Note that it's not necessary to draw anything to scale, of course, just that we note the area the circles are nominally supposed to have.)

3) P (A' and B') = 0.2, you said. This means that the area of the rectangle that's not within either circle is 0.2.

4) What you want to know is the area of the intersection of the two circles. This corresponds to the probability of A and B happening. Call this area X.

5) Finally we have four regions on our diagram that must add up to 1. We have the region exterior to the circles (0.2), circle A less its intersection with B (0.5 - X), circle B less its intersection with A (0.35 - X) and the intersection itself (X). Thus 0.2 + (0.5 - X) + (0.35 - X) + X = 1. Or, 1.05 - X = 1. Thus X = 0.05.

I guess it doesn't look that simple having spelled it all out now, but I promise you with a piece of paper it's really easy.

Cheers,
--JTR.