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Probability Mass Function For Winning the Lottery

  1. Sep 21, 2009 #1
    1. The problem statement, all variables and given/known data

    You decide to play monthly in two different lotteries, and you stop playing
    as soon as you win a prize in one (or both) lotteries of at least one million
    euros. Suppose that every time you participate in these lotteries, the probability
    to win one million (or more) euros is p1 for one of the lotteries and p2
    for the other. Let M be the number of times you participate in these lotteries
    until winning at least one prize. What kind of distribution does M have, and
    what is its parameter?

    2. Relevant equations

    Binomial Distribution: bin(n, p)
    px(k) = p(X = K) = (n choose k) * p^k * (1 -p)^(N-k) for k = 0, 1, ..., n

    Gemetric distribution: Geo(p):
    Px(k) = P(X = k) = (1-p)^(k-1)p for k = 1, 2, ...



    3. The attempt at a solution

    I'm pretty sure this is a geometric distribution.

    However, I'm not quite sure what the p is. I think it's
    p1 * (1 - p2) + p2 * (1 - p1) + p1 * p2 =
    p1 + p2 - p1p2

    so would the parameter be (p1 + p2 - p1p2)?
     
  2. jcsd
  3. Sep 21, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think you are right. Your probability at stopping at each stage is the probability of winning lottery 1 OR lottery 2. As you say, that's p=p1+p2-p1*p2. So to reach the kth stage you have have not stopped k-1 times and stopped once. (1-p)^(k-1)*p.
     
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