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? >

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.