Question 214790
I think the easiest way to understand how to find the answer is to look at a picture:
{{{drawing(400, 400, -6, 6, -6, 6, circle(-1, 0, 3), circle(2.5, 0, 2), locate(-2, 0, A), locate(1, 0, AB), locate(3, 0, B), line(-4.8, -4.8, 4.8, -4.8), line(-4.8, -4.8, -4.8, 4.8), line(-4.8, 4.8, 4.8, 4.8), line(4.8, -4.8, 4.8, 4.8)))}}}
The entire box represents the total probability, (i.e. 1), The circle labeled A represents the P(A) (which is 0.50). The circle labeled B represents P(B) (which is 0.34). And where the two circles overlap represents P(AB) (which is 0.20). So P(not A and not B) would be that part of the box not inside either circle. This area is not simply 1 minus the area of the two circles because the overlapping portion, P(AB), of the circles would be subtracted twice, in effect. To compensate for counting P(AB) twice when adding P(A) and P(B) we will subtract it once. So we will use:
P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text. Substituting in our probabilities we get:
P(not A and not B) = 1 - (0.50 + 0.34 - 0.20)
P(not A and not B) = 1 - (0.64)
P(not A and not B) = 0.36