If P(A)=0.5, P(B)=0.7 and P(A\cap B)=0.3, then what is the value of P(A'\cap B')+P(A'\cap B)+P(A\cap B')?

Explanation

The sample space consists of four mutually exclusive regions: (A\cap B), (A'\cap B'), (A'\cap B), and (A\cap B'). Their probabilities must sum to 1. The required expression covers all regions except (A\cap B). Thus, its value is 1 - P(A\cap B) = 1 - 0.3 = 0.7.

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