Suppose your water heater broke so you couldn’t take a hot shower. You go to a person and ask them to check out your water heater. That person comes to your house and uses a bunch of spare parts and then fixes it so you pay him or her for the repairs. Is this person more likely:
An accountant?
OR
An accountant and a plumber.
Did you answer a plumber? That’s understandable, but you’re wrong.
The Answer: The person is most likely an accountant.
The Explanation: When you read this word problem, you intuitively jumped to the conclusion that the person was most likely a plumber because, well, plumbers fix water heaters. BUT, the question asks what is more likely, which means it’s a probability question.
Strictly speaking, it’s more likely s/he’s an accountant than a plumber. The key to remember here is that the question asks if the person who fixes the heater is most likely an accountant or an accountant and a plumber (AKA, a plumber-accountant).
So, the probabilities are that
[A] a plumber-accountant fixed your heater (probably very small, right? Not many people are both licensed plumbers and accountants),
[B] an accountant fixed your heater (there are probs waaaaaay more accountants than plumber-accountants)
And then, in this situation, any plumber is definitely also an accountant, so you actually add those probabilities together.
A ≤ A + B
or
Plumber-Accountants ≤ Plumber-Accountant + Accountants
So, it was most likely an accountant!
