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Counter-intuitive statistics puzzles

  1. Aug 12, 2013 #1
    Recently, I came upon the Monty Hall Problem, and found it to be quite interesting. Any suggestions of similar counter-intuitive statistics puzzles would be much appreciated.
     
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  3. Aug 12, 2013 #2
    The answer is not close to 99% as one might think. In fact, it depends on how many other people are drug user? If only 0.5% of people in the group was a user, then even if someone tests positive, the chance of that person being a user is only around 33%.
    Details here
     
  4. Aug 12, 2013 #3

    micromass

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    Puzzle 1:
    In the land of Tyrannia, parents want to have boys rather than girls. So the rules of Tyrannia state that everybody who gets a girl, can have another child, until they have a boy. So for example, a couple can get a boy right away, and is then not allowed another child. But a couple can get 10 girls and then a boy, and then is not allowed another child.

    What is the eventual percentage of boys and girls?

    Puzzle 2:
    A couple has two children. One of the children is a boy. What is the probability that the other is a girl.

    A couple has two children. The oldest of the children is a boy. What is the probability that the other is a girl.

    Are these two probabilities the same?

    Other things to review: http://en.wikipedia.org/wiki/Simpson's_paradox
     
  5. Aug 12, 2013 #4

    micromass

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    How many random people do you need to gather in room in order for the probability that two have the same birthday to be 90% or higher?
     
  6. Aug 12, 2013 #5

    micromass

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    In order to get a certain tennis award, you need to play three matches. You can play against an easy player or against a very tough player. But you can't play the same player in a row.

    So you have the following two options:
    Match 1: Play against the easy player
    Match 2: Play against the hard player
    Match 3: Play against the easy player

    or

    Match 1: Play against the hard player
    Match 2: Play against the easy player
    Match 3: Play against the hard player

    To get the award, you need to win two matches in a row. Which schedule do you choose?
     
    Last edited: Aug 12, 2013
  7. Aug 12, 2013 #6

    micromass

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    You can play the following game:

    You first pay a certain sum as entry fee, namely x dollars.

    Then you flip a coin. You keep flipping a coin until you hit head. You count the amount of tails you got, call this ##n##. You get paid ##2^n## dollars.

    For example, if you throw 3 tails in a row, then you get paid ##8## dollars.

    How large should the entry fee in order for you to play this game? What if you play this game several times?
     
  8. Aug 12, 2013 #7
    Thanks alot for the suggestions micromass and I_am_learning. The puzzles defiantly seem challenging upon first glance. I'll go through each one in more depth tomorrow, as I'm awfully tired at the moment.
     
  9. Aug 12, 2013 #8

    Evo

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    Going forward nature, you must provide links to the puzzles.
     
  10. Aug 23, 2013 #9
    2 makes sense. Given that you're "very likely" to beat the easy player, you're given two chances to beat the hard player vs only 1 chance.
     
  11. Aug 23, 2013 #10
    Yeah after thinking over that puzzle thoroughly, the answer seemed rather trivial, although the appearance can be somewhat deceiving.
     
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