1. Standard memberwolfgang59
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    24 May '16 20:35
    When the Professor of Mathematics feels bored he flips two coins.
    If the result is not two heads he gets his assistant to
    run over to Student A and inform him: "Not 2 heads"
    Student A calculates that there is a 2/3 chance of a head
    and a tail and phones you up. You get to place a bet with the Prof
    (even money) that the result is a head and a tail. Fantastic!
    It's like "insider dealing"

    However, whenever the result is not 2 tails, the Prof gets his
    assistant to inform Student B.
    Student B calculates that there is a 2/3 chance of a head
    and a tail and phones you up. You get to place a bet as before.
    So whatever the coins are you will get a call informing
    you that the chance of a head and a tail is 2/3.
    Every time.

    Given that you always place your bet after a single phone call.
    What are the odds of a head and a tail?
  2. Standard memberBongalloJoe
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    25 May '16 03:47
    Originally posted by wolfgang59
    When the Professor of Mathematics feels bored he flips two coins.
    If the result is [b]not
    two heads he gets his assistant to
    run over to Student A and inform him: "Not 2 heads"
    Student A calculates that there is a 2/3 chance of a head
    and a tail and phones you up. You get to place a bet with the Prof
    (even money) that the result is a head and ...[text shortened]... at you always place your bet after a single phone call.
    What are the odds of a head and a tail?[/b]
    If you want the truth, here it is:
    I have absolutely no idea.
    BTW- i'm just curious… where do you get all of these posers?
  3. Standard memberwolfgang59
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    25 May '16 06:02
    Originally posted by Andrew Kern
    … where do you get all of these posers?
    My head.
  4. Standard memberHandyAndy
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    25 May '16 15:141 edit
    Originally posted by wolfgang59
    When the Professor of Mathematics feels bored he flips two coins.
    If the result is [b]not
    two heads he gets his assistant to
    run over to Student A and inform him: "Not 2 heads"
    Student A calculates that there is a 2/3 chance of a head
    and a tail and phones you up. You get to place a bet with the Prof
    (even money) that the result is a head and ...[text shortened]... at you always place your bet after a single phone call.
    What are the odds of a head and a tail?[/b]
    When you say "every time" do you mean that whenever there are not two heads
    (in one case) nor two tails (in another case) you will always get a phone call informing
    you that the probability of a head and a tail is 2/3?
  5. Standard memberHandyAndy
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    25 May '16 15:24
    Originally posted by wolfgang59
    My head.
    and tail?
  6. Standard memberwolfgang59
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    25 May '16 19:58
    Originally posted by HandyAndy
    When you say "every time" do you mean that whenever there are not two heads
    (in one case) nor two tails (in another case) you will always get a phone call informing
    you that the probability of a head and a tail is 2/3?
    YES.
    One of the students necessarily MUST call you after every roll of the dice.
    (Sometimes both will try to call you but you only get the info from the first)
    Whichever one calls you he correctly informs you that you have a
    2/3 chance of one of each.
  7. Standard memberwolfgang59
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    25 May '16 19:59
    Originally posted by HandyAndy
    and tail?
    That is unkind. 🙁
  8. Standard memberHandyAndy
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    25 May '16 20:32
    Originally posted by wolfgang59
    That is unkind. 🙁
    But it's only coinwise. 😉
  9. Standard memberwolfgang59
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    25 May '16 22:27
    Originally posted by HandyAndy
    But it's only coinwise. 😉
    Obversely. 😀
  10. Standard memberlemon lime
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    27 May '16 04:50
    Originally posted by wolfgang59
    When the Professor of Mathematics feels bored he flips two coins.
    If the result is [b]not
    two heads he gets his assistant to
    run over to Student A and inform him: "Not 2 heads"
    Student A calculates that there is a 2/3 chance of a head
    and a tail and phones you up. You get to place a bet with the Prof
    (even money) that the result is a head and ...[text shortened]... at you always place your bet after a single phone call.
    What are the odds of a head and a tail?[/b]
    2/3 ?
  11. Standard memberwolfgang59
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    27 May '16 18:51
    Originally posted by lemon lime
    2/3 ?
    No.
    The paradox is that we all know it is 1/2.
    Yet the students are correctly telling us it is 2/3.

    ?!?!??!?!
  12. Standard memberHandyAndy
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    27 May '16 21:48
    Originally posted by wolfgang59
    No.
    The paradox is that we all know it is 1/2.
    Yet the students are correctly telling us it is 2/3.

    ?!?!??!?!
    There are four possible outcomes: HH, TT, HT or TH. If the professor does not see two heads,
    he does see TT, HT or TH. The probability of a head and a tail is 2/3. If he does not see two tails,
    he does see HH, HT or TH -- again 2/3.

    How do you arrive at 1/2?
  13. Standard memberlemon lime
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    27 May '16 23:42
    Originally posted by HandyAndy
    There are four possible outcomes: HH, TT, HT or TH. If the professor does not see two heads,
    he does see TT, HT or TH. The probability of a head and a tail is 2/3. If he does not see two tails,
    he does see HH, HT or TH -- again 2/3.

    How do you arrive at 1/2?
    It would have to be 1/2. It's not the same as the Monty Hall problem, but the part about the students correctly assessing the probability at 2/3 threw me for a loop... I still don't see how that can be correct. Eliminating one of the outcomes will leave only 2 possible outcomes.
  14. Standard memberlemon lime
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    27 May '16 23:501 edit
    Originally posted by HandyAndy
    There are four possible outcomes: HH, TT, HT or TH. If the professor does not see two heads,
    he does see TT, HT or TH. The probability of a head and a tail is 2/3. If he does not see two tails,
    he does see HH, HT or TH -- again 2/3.

    How do you arrive at 1/2?
    The problem doesn't specify left coin/right coin, so I believe HT and TH only counts as one possible combination rather than two.
  15. Standard memberwolfgang59
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    28 May '16 00:07
    Originally posted by lemon lime
    It would have to be 1/2. It's not the same as the Monty Hall problem, but the part about the students correctly assessing the probability at 2/3 threw me for a loop... I still don't see how that can be correct. Eliminating one of the outcomes will leave only 2 possible outcomes.
    You are told
    EITHER 2 heads has NOT occurred
    OR 2 tails has NOT occurred.

    In either case there are 3 possibilities left, 2 of which are heads and tails (HT or TH)
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