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Posers and Puzzles

Posers and Puzzles

  1. 15 Jul '11 19:10
    You are given a choice of two coin flip games to play. One choice is to flip 3 coins at once, and if exactly 2 of them come up heads, you win. The other choice is to flip 4 coins at once, and if exactly 2 of them come up heads, you win. Which game do you choose to play, and why?
  2. Subscriber AThousandYoung
    It's about respect
    15 Jul '11 20:32
    1st game chance to win = 3/8
    2nd game chance to win = 6/16 = 3/8

    Seems like the same odds to me. Did I miscalculate?
  3. 15 Jul '11 20:38
    three coins:

    HHH
    HHT *
    HTH *
    HTT
    THH *
    THT
    TTH
    TTT

    Three winners out of 8

    4 coins:
    HHHH HHHT HHTH HHTT* HTHH HTHT* HTTH* HTTT
    THHH THHT* THTH* THTT TTHH* TTHT TTTH TTTT

    6 winners out of 16 = 3/8

    Yep, no gain either way
  4. 15 Jul '11 21:07
    Originally posted by iamatiger
    three coins:

    HHH
    HHT *
    HTH *
    HTT
    THH *
    THT
    TTH
    TTT

    Three winners out of 8

    4 coins:
    HHHH HHHT HHTH HHTT* HTHH HTHT* HTTH* HTTT
    THHH THHT* THTH* THTT TTHH* TTHT TTTH TTTT

    6 winners out of 16 = 3/8

    Yep, no gain either way
    That's what I got. It's easy, but a little counter-intuitive. Intuitively we can sense that the odds of exactly 2 heads start to drop off as N increases further, certainly, say, to 10 or 20.
  5. Subscriber AThousandYoung
    It's about respect
    15 Jul '11 22:13
    I pick 4 coins. That way if one of the coins lands on it's edge my odds don't go down.