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The way it was explained in the infographic wasn't clear. But what he meant is that between P(X = accountant) and P(X = accountant and plumber), the former is b

by NhanH 14y ago

The way it was explained in the infographic wasn't clear. But what he meant is that between P(X = accountant) and P(X = accountant and plumber), the former is bigger. The fact that P(X = plumber) > P(X = accountant) is irrelevant, as we wasn't concerned with P(X= plumber) at all. The implication of this "problem" is an interesting human biased: there appears to be cases where we judge the more detailed explanation as more probably, while statistically speaking, it isn't. If a person is described as "being concerned with discrimination and social justice", we tend to judge P(X = activist and Y) as more probable than P( X = Y). This is detailed in "Thinking, fast and slow" by Kahneman - a wonderful book if anyone haven't read it.

rskar 14y ago
I think you've shown me the way here. My issue, I suppose, is the problem with word problems in math. Generally that problem is two-fold. Does a word problem sufficiently describe the situation? And do you sufficiently understand the situation it describes? I believe this to be at the core of all the supposed "controversial math problems". BTW, thank you for suggesting Kahneman's book, it is now on my reading list. I did take notice that a sub-set is likely to be smaller than the set it came from: the set of all accountants vs. the sub-set of all accountants who are also plumbers. So therefore P(accountant) > P(accountant and plumber). Unless P(accountant) be zero, or P(plumber|accountant) be one, in which case neither is greater. Reflecting on my own human biases, I think I ended up reading it as if this were a multiple-choice question, and I had to pick the "best" choice. In other words, it isn't enough that this person is an accountant, but that this person is also a plumber. Or put another way, if I had to wager on whether anyone would pay just any old accountant to go mess with their water heater, I would find it more surprising that the particular accountant in fact hired had no demonstrable plumbing skills. I'd imagine Kahneman could teach me more on this. My favorite word problem joke goes something like this. If there are three cans on a fence, and you hit one with a thrown rock, how many cans remain on the fence? Answer: Two. Now, if there are three birds on a fence, and you hit one with a thrown rock, how many birds remain on the fence? Answer: None - they'd all start flying off when there's a rock hurtling towards them.

by NhanH 14y ago

rskar 14y ago

I think you've shown me the way here. My issue, I suppose, is the problem with word problems in math. Generally that problem is two-fold. Does a word problem sufficiently describe the situation? And do you sufficiently understand the situation it describes? I believe this to be at the core of all the supposed "controversial math problems". BTW, thank you for suggesting Kahneman's book, it is now on my reading list. I did take notice that a sub-set is likely to be smaller than the set it came from: the set of all accountants vs. the sub-set of all accountants who are also plumbers. So therefore P(accountant) > P(accountant and plumber). Unless P(accountant) be zero, or P(plumber|accountant) be one, in which case neither is greater. Reflecting on my own human biases, I think I ended up reading it as if this were a multiple-choice question, and I had to pick the "best" choice. In other words, it isn't enough that this person is an accountant, but that this person is also a plumber. Or put another way, if I had to wager on whether anyone would pay just any old accountant to go mess with their water heater, I would find it more surprising that the particular accountant in fact hired had no demonstrable plumbing skills. I'd imagine Kahneman could teach me more on this. My favorite word problem joke goes something like this. If there are three cans on a fence, and you hit one with a thrown rock, how many cans remain on the fence? Answer: Two. Now, if there are three birds on a fence, and you hit one with a thrown rock, how many birds remain on the fence? Answer: None - they'd all start flying off when there's a rock hurtling towards them.