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angela210793 Group Title

suppose there are 100 guys... and each of them pick any number between 0 and 100 once everybody has picked a number....you add all of the numbers and multiply that by 2/3 so...if everybody picked 100....the average would be 100 and after multiplying by 2/3, you get 66.67... now, whoever's picked number is closest to the average multiplied by 2/3, wins the game and gets $100..... what no I should I choose to maximize my chance of winning?

  • 3 years ago
  • 3 years ago

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  1. Yue27 Group Title
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    Just a stab in the dark, but if you multiplied each number by 2/3, and found the average of those. Wouldn't that be the best number to guess?

    • 3 years ago
  2. angela210793 Group Title
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    Idk....I've no idea at all :/

    • 3 years ago
  3. agdgdgdgwngo Group Title
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    Use Bayes' Theorem!

    • 3 years ago
  4. angela210793 Group Title
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    Bayes????????

    • 3 years ago
  5. agdgdgdgwngo Group Title
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    what is the most likely number that 100 guys would pick?

    • 3 years ago
  6. Ishaan94 Group Title
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    1 ?

    • 3 years ago
  7. angela210793 Group Title
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    Not getting it..........

    • 3 years ago
  8. agdgdgdgwngo Group Title
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    good! so if 100 guys pick one, then the result would be 2/3!

    • 3 years ago
  9. agdgdgdgwngo Group Title
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    so if you picked 1, then you would be winning

    • 3 years ago
  10. angela210793 Group Title
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    come on....i don't think it is solved like this guy1=59 guy2=31 . . . . . . . . . . .guy100=3 Wht now?

    • 3 years ago
  11. agdgdgdgwngo Group Title
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    alright, try having all guys pick different numbers: guy 1 pick 1, guy 2 pick 2... guy 100 pick 100

    • 3 years ago
  12. agdgdgdgwngo Group Title
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    find\[\sum_{i=1}^{100}i\]

    • 3 years ago
  13. agdgdgdgwngo Group Title
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    this is \[\frac{100*(100+1)}{2}=10100/2 = 5050\]

    • 3 years ago
  14. angela210793 Group Title
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    i did smth like |dw:1317896959755:dw|

    • 3 years ago
  15. agdgdgdgwngo Group Title
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    yes!

    • 3 years ago
  16. KorcanKanoglu Group Title
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    hmm....

    • 3 years ago
  17. angela210793 Group Title
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    silly me whn i was finding the average i divided it by 2(God knows why i did tht) and i got 1683...O.o Thnx ^^

    • 3 years ago
  18. agdgdgdgwngo Group Title
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    If you don't like that answer, set up a simulation. For every trial, make it create a list of 100 random integers. Sum those elements, divide by 100, and multiply that sum by 2./3. Repeat for about 10000-1000000 trials, adding the results of each trial together, and finding the average result.

    • 3 years ago
  19. angela210793 Group Title
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    |dw:1317897551125:dw|

    • 3 years ago
  20. agdgdgdgwngo Group Title
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    yep, I got the same 33.3 answer after 10000 trials

    • 3 years ago
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