Start with plain language: we want the probability that neither A nor B will occur, which is equivalent to saying that we have not-A
AND not-B.
In formal notation:
P(-(AvB)) = P((-A)^(-B))
The probability of not-A is simply the inverse: 1-0.54 = 0.46
The probability of not-B is simply the inverse: 1-0.68 = 0.32
The probability of both together is P((-A)^(-B)) = P(-A)*P(-B) = 0.46*0.32, but that isn't what the question is asking
.
Remember that we need BOTH to happen, and this is clear when it asks for the
greatest value of the probability. In fact, we are limited by probability of not-B, because of we don't achieve
not-B, we don't reach our goal.
Therefore, the greatest probability for reaching not-B will be our greatest probability that neither of the two will occur: that is,
answer B.This is pure concept, but you can get the answer extremely quickly if you see what the question is really asking.