Timeline for Do I have a misconception about probability?
Current License: CC BY-SA 4.0
42 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2023 at 12:38 | audit | First questions | |||
| Aug 20, 2023 at 12:39 | |||||
| Aug 18, 2023 at 0:11 | audit | First questions | |||
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| Aug 15, 2023 at 14:03 | audit | First questions | |||
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| Aug 3, 2023 at 2:20 | audit | First questions | |||
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| Jul 31, 2023 at 11:26 | audit | First questions | |||
| Jul 31, 2023 at 11:32 | |||||
| Jul 29, 2023 at 8:59 | audit | First questions | |||
| Jul 29, 2023 at 9:10 | |||||
| Jul 27, 2023 at 18:11 | answer | added | user801306 | timeline score: 0 | |
| Jul 27, 2023 at 12:17 | comment | added | PJTraill | @screwtop Quite so, and the page is directed at teachers, who are presumed to understand, at the latest when they read “which is not the right answer”. | |
| Jul 27, 2023 at 2:17 | comment | added | screwtop | I like the question, though to be fair on the source page, it does state that "there are so many misconceptions that it would be impossible to list them all, let alone analyze them", and "To a first approximation, with isolated exceptions, the best policy is to teach the correct concepts and move on." | |
| Jul 26, 2023 at 18:07 | vote | accept | Lukasz Skowron | ||
| Jul 26, 2023 at 15:30 | comment | added | jrdevdba | Interesting puzzle that I'd be sure to get wrong. But I do see a problem with the phrase "on average" in this case. Think about it. After the 100th step, you are where you are, period. There is no "average" about it. It's like saying, after I take the subway uptown two stops and downtown 3 stops, how far away, on average, am I from my original stop? You just are where you are, which is an absolute distance from where you started. Seems to me that is thrown in to make it a trick question. | |
| Jul 26, 2023 at 14:03 | comment | added | Daniel Martin | I suspect that the fundamental misconception the author is trying to point to is that people will often conflate "f(average of x)" and "average of f(x)", for arbitrary function f. (In this case, f(x) = abs(x)) There are likely better examples that the author could have chosen. | |
| Jul 25, 2023 at 20:54 | comment | added | java-addict301 | Or does the author have a misconception (or no conception at all) of the Coriolis effect? | |
| Jul 25, 2023 at 20:44 | answer | added | Philip Roe | timeline score: 2 | |
| Jul 25, 2023 at 20:20 | comment | added | JonathanZ | What an irritating bit of math writing. It's not "probability" that misconception is about, it's a confusion between "signed displacements" and "distances". And if ever an English sentence could have a smug look on its face, that last sentence would have one. | |
| Jul 25, 2023 at 16:53 | comment | added | Filip Milovanović | To be honest, I don't know if this qualifies as a "misconception". The wrong answer doesn't arise from some misbelief or some inadequate conceptualization of probability, but simply from not paying attention to the wording of the question and/or from the question(er) not placing more emphasis on what's being asked of you. The misconception aspect of it would be more related to what people expect the average distance vs average location to be (as in, do they expect them to be the same or different, and why). | |
| Jul 25, 2023 at 16:18 | comment | added | Philip Oakley | It is a classic case of imprecise English that initially suggests mathematical precision (with a positive or negative value measured Northwards for the distance moved) and yet flips over to the imprecise choice of North or South (distance 'far away' from origin). Our brains fail to spot the subtle mind shift and try harder to fit the discussion to our mistaken axioms. Most paradoxes use the same trick (Monty Hall) | |
| Jul 25, 2023 at 6:44 | audit | First questions | |||
| Jul 25, 2023 at 6:53 | |||||
| Jul 24, 2023 at 23:25 | answer | added | jmoreno | timeline score: 3 | |
| Jul 24, 2023 at 20:19 | history | edited | user | CC BY-SA 4.0 |
added 3 characters in body
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| Jul 24, 2023 at 20:03 | comment | added | Glenn Willen | I think "how far away am I, on average" is a colloquial phrasing that's reasonable to interpret as meaning the second thing, and not the first thing. But I don't like using it as a "gotcha" when the first possible meaning is there to confuse things. | |
| Jul 24, 2023 at 20:01 | comment | added | Glenn Willen | I agree with you that the phrase "on average" is problematic here, although I think the popular misconception would not vanish with a more careful phrasing. "Considering the distribution over endpoints of random walks, how far is the average of that distribution from the origin?" Zero. "Considering the distribution over distances of random walk endpoints from the origin, what is the average of that distribution?" Assuming 'average' here is the mean, nonzero, as explained in various answers. (Although the mode of the distribution is zero -- no individual distance will be more common than zero.) | |
| Jul 24, 2023 at 19:38 | answer | added | Caleb | timeline score: 12 | |
| Jul 24, 2023 at 17:25 | answer | added | DotCounter | timeline score: 7 | |
| Jul 24, 2023 at 13:04 | answer | added | Don Hatch | timeline score: 22 | |
| Jul 24, 2023 at 12:28 | answer | added | Ennar | timeline score: 6 | |
| Jul 24, 2023 at 12:27 | comment | added | Henry | Related: math.stackexchange.com/questions/103142/… | |
| Jul 24, 2023 at 12:06 | answer | added | plm | timeline score: 24 | |
| Jul 24, 2023 at 11:26 | answer | added | Martigan | timeline score: 9 | |
| Jul 24, 2023 at 10:14 | comment | added | Falco | "Do I have a misconception about probability?" - probably ;-) | |
| Jul 24, 2023 at 7:21 | history | became hot network question | |||
| Jul 24, 2023 at 2:11 | review | Close votes | |||
| Aug 1, 2023 at 3:08 | |||||
| Jul 23, 2023 at 23:51 | comment | added | Masacroso | Oh, I see. Thank you for the clarification @Xander | |
| Jul 23, 2023 at 23:47 | review | Low quality posts | |||
| Jul 24, 2023 at 2:40 | |||||
| Jul 23, 2023 at 23:46 | comment | added | Xander Henderson♦ | @Masacroso No. We are not talking about the expected location after $n$ steps, we are talking the average distance. At step 2, for example, you could be 2 steps away (TT or HH), or you could be at your starting location (HT or TH). All four outcomes are equally likely, hence the expected distance is $(2+2+0+0)/4 = 1$ unit from the starting location. More generally, after $n$ steps, there is a non-zero chance of being somewhere other than the start, hence a non-zero (positive) expected distance from the start. | |
| Jul 23, 2023 at 23:44 | comment | added | Masacroso | I didn't see any missconception here: the expected distance from the origin will be zero as far as the probability of heads and tails is the same, that is, $1/2$ | |
| Jul 23, 2023 at 23:41 | answer | added | Vincent Batens | timeline score: 38 | |
| Jul 23, 2023 at 23:39 | comment | added | John Douma | If the question asked for the expected position then the common misconception would be correct. I would classify the "misconception" as a misinterpretation of the problem. | |
| Jul 23, 2023 at 23:39 | comment | added | Xander Henderson♦ | "In a way it is pointless to talk about misconceptions, when you don't explain the misconceptions." The linked page contains, in section 4, a very long list of "misconceptions". None of them are explained. A few have references. These are listed as misconceptions held by professionals, hence one might expect that the intended audience would be capable of using the Google for details. | |
| Jul 23, 2023 at 23:34 | comment | added | lulu | The distance from where you start is the absolute difference. That is, if you are moving on the number line, and you are at $-3$, the distance from $0$ is $3$. Hence the answer is clearly not $0$ here. | |
| S Jul 23, 2023 at 23:21 | review | First questions | |||
| Jul 23, 2023 at 23:42 | |||||
| S Jul 23, 2023 at 23:21 | history | asked | Lukasz Skowron | CC BY-SA 4.0 |