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Independent Events Question: Coin Tossing!

  1. Feb 16, 2009 #1
    Hello all,

    I am working on this problem, have searched my textbook, this forum, etc and am still as lost. I suspect I need to (in some form) use the formula P(AB)/P(B) = P(A) as it is the integral formula of this section. Any suggestions or hints are greatly appreciated.

    A fair coin is tossed until a head is obtained for the first time. If this experiment is performed 3 times, what is the probability that exactly the same number of tosses will be required for each of the 3 performances?

    Note: the answer is 1/7

    My work thus far:

    I know n-1 tails must be obtained in each performance

    Events:
    Ai = a head is obtained on the ith trial
    Bi = " " tail " "
    P(Ai) = 0.5
    P(Bi) = 0.5
     
  2. jcsd
  3. Feb 16, 2009 #2
    Well, the lenght of the first sequence may be 1 , 2 , 3 , etc...

    Suppose the lenght of the first sequence is 1 (you got a head at the first toss).
    Then, what is the probability of obtaining again the same sequence 2 more times?

    And if the lenght of the first sequence was 2 , what would be the probability of repeating the results 2 more times?

    And if the lenght was 3?

    And then, finally, you should sum all this parcels...
     
  4. Feb 16, 2009 #3
    Thank you, that was very helpful!
     
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