Two events A and B satisfy P(A) = 0.6, P(B) = 0.35 and P(A given B) = 0.4. Find P(A or B).

The conditional probability supplies the overlap: from $P$(A given B) = $P$(A and B) ÷ $P$(B) we get $P$(A and B) = $0.4\times 0.35=0.14$. The addition rule then gives $P$(A or B) = 0.6 + 0.35 − 0.14 = 0.81. The value 0.95 adds the two probabilities without subtracting the overlap, so it double-counts it — that would be the answer only for mutually exclusive events, and these are not, since their overlap is 0.14. The value 0.74 treats the events as independent and subtracts $P(A)\times P(B)=0.21$ instead; they are not independent, because $P$(A given B) = 0.4 differs from $P(A)=0.6$, so knowing $B$ happened makes A less likely. The value 0.14 is the overlap itself, a step in the working rather than the answer.