SOLUTION: For two events the probabilities are as follows: P(A)=0.50, P(B)=0.34, P(AB)=0.20. Determine P(not A and not B). I want to determine if I did the problem correctly. Could you pl

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Question 214790: For two events the probabilities are as follows: P(A)=0.50, P(B)=0.34, P(AB)=0.20. Determine P(not A and not B).
I want to determine if I did the problem correctly. Could you please show me how you get the answer. Thanks
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
I think the easiest way to understand how to find the answer is to look at a picture:

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