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Geometric distribution problem

  1. Jan 18, 2010 #1
    Can anyone solve this for me? I think it is geometric distribution.

    Tom, Dick and Harry play .the following game. They toss a fair coin in
    turns. First Tom tosses, then Harry, then Dick, then Tom again and so on
    until one of them gets a Head and so becomes the winner. What is the
    probability that Tom wins?
  2. jcsd
  3. Jan 18, 2010 #2


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    Welcome to PF!

    Hi danniim! Welcome to PF! :wink:

    Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
  4. Jan 18, 2010 #3
    Hi tiny-tim,

    Okay well my main problem is that I don't know what formula to use.

    I thought you would use p(q)^x-1 where p is the probability of success(0.5) and q is the probability of failing (0.5), x is supposed to be the number of trials ie the number of times the coin is tossed but this is not given. This leaves me with the following:

    0.5(0.5)^x-1 = ?..... two unknowns.

    So clearly I am not understanding something in the question.
  5. Jan 18, 2010 #4


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    Hi danniim! :smile:

    (use n, not x, for numbers, and try using the X2 tag just above the Reply box :wink:)

    Yes, you use pqn-1 for the probability of the game finishing on the nth toss.

    Now add up for all the n's that make Tom the winner. :wink:
  6. Jan 18, 2010 #5
    Thanks! :)
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