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Coin is tossed 3 times

  1. Jan 10, 2009 #1
    Qst A).

    A coin is tossed 3 times and you note that the coin lands heads exactly twice. What is the probability that the first toss was the tail?


    I know how to do it logically but not with all the notation.

    Any help appreciated.

    Thanks
     
    Last edited: Jan 10, 2009
  2. jcsd
  3. Jan 10, 2009 #2

    HallsofIvy

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    Re: Probability

    That trick didn't work when you posted this in "homework"- it won't work here!
     
  4. Jan 10, 2009 #3

    mathman

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    Re: Probability

    It looks like the answer should be 1/3, since there is nothing to favor any one of the three tosses over any other.
     
  5. Jan 11, 2009 #4

    HallsofIvy

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    Re: Probability

    If the problem had said "what is the probability the first coin was a tail" would you also answer "1/3"? Since "heads" or "tails" is all there can be, what does the remaining "1/3" probability represent?

    tictac123, since you say you were able to do this "logically", what answer did you get?
     
  6. Jan 11, 2009 #5

    mathman

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    Re: Probability

    Since the condition is that 2 tosses came up heads, the probability that the first toss was heads is 2/3.
     
  7. Jan 12, 2009 #6

    HallsofIvy

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    Re: Probability

    There are 8 possible outcomes for three coins, and you can list them:
    HHH
    HHT
    HTH
    HTT
    THH
    THT
    TTH
    TTT
    Of those, exactly 4 have two "H"s, HHT, HTH, and THH. Of those 3, 2 have "H" first.

    I would still like to know what tictac123 means by "I know how to do it logically but not with all the notation."
     
  8. Jan 12, 2009 #7
    Re: Probability

    A solution exists?
     
  9. Jan 15, 2009 #8
    Re: Probability

    exactly "3" have two heads
     
  10. Jan 15, 2009 #9
    Re: Probability

    No 4 have 2 heads, HHH, HTH, HHT, THH. Out of them 3 have exactly 2 heads
     
  11. Jan 16, 2009 #10
    Re: Probability

    It's 1/3. You can even use Bayes' sentence, but it might be overkill in this case since HallsofIvy's list says it all (but it's a good exercise to double-check it using Bayes' sentence).
     
  12. Jan 20, 2009 #11
    Re: Probability


    Who are you quibbling with, him or me ? He cites three as evidence of four. Obviously the issue is whether the intention was exactly two heads or two or more heads, but I'm just referring to his statement
     
    Last edited: Jan 20, 2009
  13. Jan 20, 2009 #12
    Re: Probability

    Probably you since to me "exactly 3 have 2 heads" doesn't mean exactly 2 heads since you put "exactly" before the 3.
     
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