“Last week, the heat in my apartment crapped out because my water heater broke. I went to a person, showed him the water heater, he used a bunch of spare parts and then fixed it. I paid him for the repairs.”
Is this person more likely: An accountant?
or An accountant and a plumber?
Solution
It’s more likely that he’s an accountant.
Since the scenario makes it sound like the guy is a plumber, you intuitively thought that he’s a plumber. However, anyone who is “an accountant and a plumber” is also an accountant. Think of it like this:
Strictly speaking, it’s more likely that he’s an accountant than a plumber because the probability “A” that the guy who fixed the water heater is both an accountant and a plumber is already factored into the probability that the guy who fixed my water heater is an accountant:
There’s also the probability “B” that the guy who fixed the water heater is only an accountant and not a plumber:
The probability A is the probability that a plumber-accountant fixed my water heater. The sum of the two probabilities A and B is the probability that an accountant fixed my water heater.
Since A ≤ A + B, probabilistically it’s more likely that the guy who fixed my water heater is an accountant than it is that he was an accountant and a plumber.
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