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Probability Puzzle — Parallax Forums

Probability Puzzle

Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
edited 2011-10-29 04:57 in General Discussion
Found this one on Reddit:
If you choose an answer to this question at random, what is the chance you will be correct?
A) 25%
B) 50%
C) 60%
D) 25%

(I hereby disclaim responsibility for whatever migraines this might cause. And, no, I have not figured out the answer yet myself.)

-Phil

Comments

  • ElectricAyeElectricAye Posts: 4,561
    edited 2011-10-27 14:00
    I've got 4 choices, so if they were all different, I would have a 25% chance of being right.
    But I've got two choices that are the same, and both are chances of hitting 25%, which would mean I've got a 50% of getting the right answer.
    But the chance of hitting the right answer of 50% is only 1 out of 4, so..... so..... uh... uh...

    Was this sponsored by the people who make Advil?

    EDIT: what would happen if you made choice C equal to 0% ?
  • xanatosxanatos Posts: 1,120
    edited 2011-10-27 14:09
    This is one of those things I love, and am completely comfortable allowing the mystery to be... :-)

    Dave
  • Dave HeinDave Hein Posts: 6,347
    edited 2011-10-27 14:52
    zero percent
  • bill190bill190 Posts: 769
    edited 2011-10-27 16:12
    33 1/3 percent chance?
  • Martin_HMartin_H Posts: 4,051
    edited 2011-10-27 16:44
    If you say 25% you have a 50% chance of being correct, and 50% and 60 have a 25% chance of being correct.

    Average Probability = (50% + 25% + 25%) / 4 = 25%
  • Dave HeinDave Hein Posts: 6,347
    edited 2011-10-27 17:15
    The problem statement is "If you choose an answer to this question at random, what is the chance you will be correct?" The chance is 0% because none of the choices is the correct answer, which is 0%.
  • mparkmpark Posts: 1,305
    edited 2011-10-27 17:41
    Phil Pilgrim (PhiPi) wrote: »
    Found this one on Reddit:

    How the heck can you read Reddit and still be so productive??!

    Must go refresh Reddit now.
  • ElectricAyeElectricAye Posts: 4,561
    edited 2011-10-27 18:07
    Dave Hein wrote: »
    ... The chance is 0% because none of the choices is the correct answer, which is 0%.

    But couldn't one of the choices be 0% and you would still be wrong?

    If choice C were 0%, then you'd have a 25% chance of selecting C. Right?

    And since two of the choices are 25%, that gives you double the chance of getting it right. Right?

    And since double 25% is 50%, then....

    Maybe there's no right answer, which might be saying something different than saying 0%. But then what does it mean?

    http://www.youtube.com/watch?v=OQSNhk5ICTI
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-10-27 18:15
    mpark wrote:
    How the heck can you read Reddit and still be so productive??!
    Browser demands equal time on AnimalPlanet. That's when I get my work done.

    -Phil
  • W9GFOW9GFO Posts: 4,010
    edited 2011-10-27 18:18
    ElectricAye wrote: »
    But then what does it mean?

    http://www.youtube.com/watch?v=OQSNhk5ICTI

    Oh man, little warning next time?
  • lanternfishlanternfish Posts: 366
    edited 2011-10-27 18:57
    The answers 25%, 50% and 60% are of no importance. It is either A, B, C, or D. Typed with the confidence of someone who doesn't know the answer!:blank:
  • Dr_AculaDr_Acula Posts: 5,484
    edited 2011-10-27 19:07
    When in doubt, choose "C". It got me through medical school...
  • lanternfishlanternfish Posts: 366
    edited 2011-10-27 19:27
    Couldn't resist reading Reddit. And my brain imploded. So off to do something mindless!
  • jmgjmg Posts: 15,185
    edited 2011-10-27 20:15
    Hehe - nice one. The question is actually entangled with the answer, so it fails as a proper question.
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-10-27 21:02
    jmg wrote:
    The question is actually entangled with the answer, so it fails as a proper question.
    Maybe the answer is the limit of an infinite series that has to be arrived at recursively.

    -Phil
  • mindrobotsmindrobots Posts: 6,506
    edited 2011-10-28 05:32
    I've read the problem several times and randomly have chosen not to answer it each time. Luckily, that sample space fits well within a random distribution, so I'm still good to go!!
  • Dave HeinDave Hein Posts: 6,347
    edited 2011-10-28 06:02
    There must be something I'm missing, because this "puzzle" doesn't seem that puzzling. There are 5 possible ways to state this puzzle that have solutions. The possible solutions would be 0%, 25%, 50%, 75% and 100%. The choices would need to include the answer 0, 1, 2, 3 or 4 times.

    The way the puzzle is stated in the original post the answer would be zero.

    EDIT: Changed "6 possible ways" to "5 possible ways".
  • ajwardajward Posts: 1,130
    edited 2011-10-28 06:42
    The correct answer isn't listed. Everyone knows the answer to life, the universe and everything is... 42. ;-)

    @
  • Martin_HMartin_H Posts: 4,051
    edited 2011-10-28 07:16
    Maybe I misread the puzzle, but I read this as an external event was going to happen with a certain probability. If you picked an answer randomly (a, b, c or d), what is the probability that your randomly chosen answer would be the correct answer to describe the probability of the external event. I assumed that the probability of external event was known and one of the choices. In any event the question itself was really confusing.
  • MicrocontrolledMicrocontrolled Posts: 2,461
    edited 2011-10-28 07:36
    Actually, if someone was reading this it would appear to have 3 choices, making the probability about 33% (e.g, if you thought this through in your head, it would not be thought of as "25, 50, 75, or 25" but rather "25, 50, or 75").
  • bill190bill190 Posts: 769
    edited 2011-10-28 10:52
    Microcontrolled wrote: »
    Actually, if someone was reading this it would appear to have 3 choices, making the probability about 33% (e.g, if you thought this through in your head, it would not be thought of as "25, 50, 75, or 25" but rather "25, 50, or 75").

    As I see it, right so far. It says "what is the chance". So the answer to that does not need to be one of the answers given...

    Next path you can take is... Are any of the answers correct?

    Or another path you can take is that you could randomly choose 25%. Since that answer is given twice, you have a greater chance of choosing that answer! So the question is...

    Is 25% the correct answer? If yes, then you would have a higher percentage chance of choosing the correct answer.

    If 25% is not correct, then you would have a lower percentage chance of choosing the correct answer.

    So that 33 1/3 chance should be adjusted up/down to reflect that.

    I guess you could assume that 25% was the correct answer, then figure that in and see what you get.

    And then assume that 25% was the wrong answer, then figure that in and see what you get.
  • David BDavid B Posts: 592
    edited 2011-10-28 11:30
    So you randomly choose one of A, B, C or D.

    There is a 50% chance of choosing 25% so either A or D has a 0% chance of being correct.
    There is a 25% chance of choosing 50% so choosing B would also have a 0% chance of being correct.
    There is a 25% chance of choosing 60% so choosing C would also have a 0% chance of being correct.

    Result: if you choose an answer at random then there is a 0% chance you'll be correct.

    disclaimer: this is a total guess.
  • bill190bill190 Posts: 769
    edited 2011-10-28 12:59
    0% sounds right to me...

    So what if you changed the problem to the following...
    (Sorry for doing this, but I could not resist! :smile: )
    If you choose an answer to this question at random, what is the chance you will be correct?
    A) 0%
    B) 50%
    C) 60%
    D) 0%
  • ElectricAyeElectricAye Posts: 4,561
    edited 2011-10-28 13:09
    Or how about this one:

    If you choose an answer to this question at random, what is the chance you will be correct?

    A) 0%
    B) 50%
    C) The question is meaningless.
    D) 25%
  • MicrocontrolledMicrocontrolled Posts: 2,461
    edited 2011-10-29 04:57
    Answer is C.
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