Here's another one of those simple problems (I’ve cited before) where language gets in the way!….
Walter Hickey posted a dozen old classic math problems in nice big graphic form:
[these dozen examples offer some good ones for primary/secondary students, and youngsters are especially susceptible to the following 'broken water heater' fallacy.]
#6 he calls “The Broken Water Heater Problem”… I’ve seen it in many forms, and there are a zillion ways to set it up. Hickey posts it as follows (quoting verbatim):
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 and a plumber?
Even if you’re not familiar with these type-questions, hopefully upon a moment of logical thought the reader recognizes the answer should be that the person is “an accountant.”
The problem is, often people DON'T really give a moment of ‘logical thought,’ instead jumping to the conclusion that it's more likely (more probable) that the individual must have plumbing skills, and thus must be “an accountant and a plumber.” But of course ANYone who is ‘an accountant and a plumber’ is automatically ‘an accountant’ — in Venn diagram terms, the circle of accountants includes wholly within it the circle of ‘accountants and plumbers.’
Again, I just like this because it once more demonstrates how easily words and language often short-circuit, rather than aid, our logic. [In fact, I dare say our latest election is clearly another example of mere visceral words/language overriding reason.]