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Fair Coin Qst

  1. Oct 24, 2007 #1
    "A fair coin is flipped repeatedly. What is the probability that the 5th tail occurs before the tenth head?"

    What I have so far:

    So the 5th tail has to come before 10th head. So if we take getting a tails as success and after the 9th head, we MUST have 5 tails --> we can only have 14 flips or less(but more than 4, since we're looking for 5 Tails).

    let X be the # of flips required to get a 5th tail and since X is a negative binomial rv(conditions above, hopefully)

    The lower bound on the sum is 5, and the upperbound on the sum is 14. (n-1)C4 is n-1 "CHOOSE" 4

    [tex]\sum[/tex]P(X=n) = [tex]\sum[/tex][(n-1)C(4)](0.5)[tex]^{5}[/tex](0.5)[tex]^{n-5}[/tex]

    I don't know if I am doing this right because I am not 100% sure if X is a negative binomial RV. Can anyone maybe explain the setting up process or something.

  2. jcsd
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