The likelihood of being an accountant vs being an accountant and a plumber This is a very interesting word problem that I came across in an old textbook of mine. So I know it's got something to do with probability, but other than that, the textbook gave no hints really and I'm really not sure about how to approach it. Probability has always given me headaches but in fact, I've been racking my head over it so long that I've got a huge headache. Any guidance hints or help would be truly greatly appreciated.

"Last week, the heat in my apartment crapped out because my water heater broke.
I went to a person, showed him the water heater and asked him to fix it."
Ignoring the practicality side of this problem and instead focusing on the math probability side of it,
Is this person more likely:

*

*An accountant

OR

*

*An accountant and a plumber?


 A: Simple set theory, being an accountant and a plumber is a subset of being an accountant, so the probability of being an accountant is greater.
To put it in other words, every person who is an accountant and a plumber is indeed an accountant! But not all accountants are also plumbers. 
A: I've seen this kind of question and answer before. Let me venture a contrary (Bayesian) opinion.
The story gives you important prior information - you already know he's a plumber (with very high probability - he might just be a talented amateur). With that prior information, the universe consists only of plumbers. In that universe the probability of (accountant and plumber) is essentially the same as the probability of (accountant). It's probably pretty low.
Framing the question as an instance of the conjunction fallacy asks you to ignore the fact that you know he's a plumber.
The point of my answer is to try to save the OP from his comment:

God I'm so dumb...I always confuse myself over the simple questions.
  Now it makes sense. –  anonymous 19 hours ago

The letter of the probability laws say the answer is as @DonkeyKong correctly notes. I'm looking for a formulation that is mathematically defensible and matches common sense. In answer to @Rahul 's comment, consider a weighted average. Suppose the probability that the repairman is a talented amateur is 0.01. That's the case in which the probability of (A and P) is less than the probability of P. The other 99% of the time the probability of P is 1 and the probability of (A and P) is the probability of A in the universe of plumbers, which is much less than 1.
