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Die throwing probability question

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Problem:
    Suppose in a certain game a player receives $1 for each "five"
    and each "six" thrown on a single die.
    a. If the die is thrown six times, find the mean and variance of
    the amount the player receives.
    b. If the player throws repeatedly until he gets $10, find the
    mean of the number of throws necessary



    2. Relevant equations



    3. The attempt at a solution
    Attempt:
    I think this is binomial. Then:
    1a)
    n=6
    p=2/6 = 1/3
    mean = n*p = 2
    variance= n*p*(1-p) = 6*1/3*2/3 = 1/3
    Is this correct?

    1b)
    If $10 is the amount gained,it means:
    x=10 (successes)
    n=trials
    p=1/3
    1-p=2/3

    => {n!/[x!(n-x)!]}*(p^10)*(1-p)^(n-10) ???
    Is this correct, although tedious?

    Thank you very much for any help.
     
  2. jcsd
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