You're certainly right about the details you mentioned. But they are not relevant to the problem. "Accountant and not a plumber" was not in the question at all.

You're certainly right about the details you mentioned. But they are not relevant to the problem. "Accountant and not a plumber" was not in the question at all. Lets make it more precise. X = is accountant, Y = is plumber. The question is which is greater: P(X) or P(X and Y). It should be clear that the event "X and Y" is completely contained within the event "X". To put it another way, P(X) = P(X and Y) + P(X and ~Y) (we are summing over all possible unconstrained events, in this case Y and ~Y). Hence, P(X) >= P(X and Y)