Two events A and B with probability 0.5 and 0.7 respectively have joint probability of 0.4 The probability that neither A nor B happens is?

Let me denote -A as the event that A does not happen. So we want Pr[-(A and B)]

Now, the event that neither A nor B occurs is the opposite of either A occurring, or B occurring or both occurring.

So Pr[-(A and B)] = 1 - Pr(A or B)= 1 - [Pr(A) + Pr(B) - Pr(A and B)] (since A+B is double counted)= 1 - (0.5 + 0.7 - 0.4)= 1 - 0.8= 0.2