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I have 22 underpants in the drawer and it is dark and I cannot identify the colors. 3 pairs are red.

What is the probability of my putting on a red pair of underpants from the drawer?

3/22 is the wrong answer.

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closed as unclear what you're asking by dcfyj, Glorfindel, JMP, Sconibulus, Beastly Gerbil Mar 29 '17 at 20:17

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    $\begingroup$ 3/11? What do you mean by 3 pairs? Is that 6 or 3 individuals? $\endgroup$ – Beastly Gerbil Mar 29 '17 at 17:43
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    $\begingroup$ Why they are called pairs even though they are singles? itself is much discussed question :-) $\endgroup$ – Techidiot Mar 29 '17 at 17:51
  • $\begingroup$ @Techidiot "And pants (pantaloons) were originally two like things. You put them on one leg at a time because they actually came in two pieces. You put on one leg, tied it around your waist, then put on the other. From the beginning, about the 16th Century, pants have been referred to as a pair." $\endgroup$ – n_plum Mar 29 '17 at 17:57
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The answer is:

100%. You put on 20 pairs of underpants. With only two left you must be wearing a pair of red underpants.

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  • $\begingroup$ But you put on a pair of underpants, singular, not plural $\endgroup$ – Beastly Gerbil Mar 29 '17 at 17:48
  • $\begingroup$ @BeastlyGerbil If he put on all pairs of underpants, he did, indeed, put on a pair of red underpants. $\endgroup$ – Ben Richards Mar 29 '17 at 17:49
  • $\begingroup$ This is the clever answer I used to give people, but strictly speaking there is a more detailed answer that is even more correct. $\endgroup$ – Clint Eastwood Mar 29 '17 at 17:49
  • $\begingroup$ @BenRichards hmm I suppose so $\endgroup$ – Beastly Gerbil Mar 29 '17 at 17:49
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X*Y/Z, where X is the probability that you put on a pair of underpants from the drawer in the first place, Y is the total number of red underpants, which is at least 3, and Z is the total number of underpants of any color, which is at least 22.

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  • $\begingroup$ closer to the correct answer. $\endgroup$ – Clint Eastwood Mar 29 '17 at 18:04
  • $\begingroup$ Total number of red pants is explicitly mentioned to be 3 pairs. How do you get at least 3? $\endgroup$ – Sid Mar 29 '17 at 18:10
  • $\begingroup$ Given the close-to-correctness of my previous answer, the statement "3 pairs are red" could be interpreted loosely to be correct even if more than 3 pairs are red. $\endgroup$ – paramesis Mar 29 '17 at 18:16
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3/11, because you have "22 underpants", meaning "11 pairs of underpants".

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  • $\begingroup$ Pair is just a reference, as in pair of jeans. That means 1 article of clothing, not two in that sense. Unless it's a trick question $\endgroup$ – n_plum Mar 29 '17 at 17:50
  • $\begingroup$ @n_palum: Yeah, that's what I thought. $\endgroup$ – Deusovi Mar 29 '17 at 17:52
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Zero percent probability

because

in the dark (with no light), all of them are black.

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    $\begingroup$ Something doesn't change colour because its dark, it just looks a different colour $\endgroup$ – Beastly Gerbil Mar 29 '17 at 17:45
  • $\begingroup$ 3/22 would be statistically correct. So I could only imagine that it was a trick question. Therefore, as color is simply determined by how light reflects off of the object, and if there is no light, they're effectively black. That's my reasoning. $\endgroup$ – Ben Richards Mar 29 '17 at 17:47
  • $\begingroup$ @BeastlyGerbil May be that is non lateral way of thinking(as the site is puzzling itself). We can't deny that $\endgroup$ – L.K. Mar 29 '17 at 17:47
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Here is another try.

We have 22 underpants of which 3 are red - but maybe more. If there could be any number of red underpants, we would have 20 scenarios:


  1. 3 red / 19 non-red
  2. 4 red / 18 non-red
  3. 5 red / 17 non-red
  4. 6 red / 16 non-red
  5. 7 red / 15 non-red
  6. 8 red / 14 non-red
  7. 9 red / 13 non-red
  8. 10 red / 12 non-red
  9. 11 red / 11 non-red
  10. 12 red / 10 non-red
  11. 13 red / 9 non-red
  12. 14 red / 8 non-red
  13. 15 red / 7 non-red
  14. 16 red / 6 non-red
  15. 17 red / 5 non-red
  16. 18 red / 4 non-red
  17. 19 red / 3 non-red
  18. 20 red / 2 non-red
  19. 21 red / 1 non-red
  20. 22 red / 0 non-red

Total number of possibilities in all scenarios: 250 red /190 non-red


As far as we know, we could be in any of the 20 scenarios picking any of the 22 underpants, so we have 20 * 22 = 440 different possibilities. Since 250 of the possibilities gives us a red pair of underpants, we get the answer:

250/440 = 25/44 = 57%

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