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Isn't it absurd?

$\textbf{Problem-}$ Suppose my water heater broke and heat in my apartment raised high. I went to a "person" to ask him to take a look at it, he came to my apartment, used a bunch of spare parts and then fixed it. I paid him for the repairs."

Now what is more likely,

$1)$ He is a mathematician,

$2)$ He is a mathematician and plumber.

Now look at this Image where, A (white) means he is both mathematician and plumber and B (yellow) means he is only a mathematician and not a plumber.

enter image description here

Now probability A means that a mathematician plumber fixed my water heater, and probability B means a mathematician who is not a plumber fixed it, Now since A $\leq$ A+B, it is more likely that a mathematician fixed my water heater. Isn't it absurd.

But if I denote B by plumbers who are not mathematicians, I get it is more likely a plumber fixed my water heater, so which one is more likely?

Martin Sleziak
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Bhaskar Vashishth
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2 Answers2

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sure, if those are the only two options you are comparing, anything not plumber+plumber is more likely than anything not plumber alone. The flaw in the logic is that you don't compare either to the far more likely probability of plumber and not mathematician :) .

So no, it doesn't make probability absurd, it makes that particular comparison absurd, since it discounts the most probable outcome of plumber+ not mathematician.

(addendum for clarity)

The flaw here is what you showed is NOT what the title of the question said: You're not comparing "Mathematician" to "plumber", you're comparing "mathematician+plumber" to "mathematician"

Alan
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  • how is plumber+non-mathematician more probable than non-(purple elephant with phd in dog-walking)? – Asinomás Oct 02 '14 at 04:07
  • Plumber+non mathematician is pretty much the most likely possibility for "the person who came over and did my plumbing job and took money for it". Now, comparing that to Plumber+non (other thing) is another question, but I'm only considering adding 1 other condition at a time – Alan Oct 02 '14 at 04:09
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The Conjunction fallacy. See Wikipedia. It's not probability that's absurd, it's ... (it's really hard to put this in a nice way...)

Robert Israel
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