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Geometric Distribution Probability problem

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data

    We roll a fair die until we get a three or a four. Z denotes the number of rolls needed. What is the probability that Z >= 3? (replacement assumed)

    2. Relevant equations

    Geometric distribution seems logical here?

    3. The attempt at a solution

    Let p(A) = p(getting a three) = 1/6 and p(B) = p(getting a four) = 1/6. We want p(A U B) = 1/3 (a three OR a four). Correct?

    Now, we know p(Z >= k) = (1 - p)^(k - 1). Is that enough for this question? I got 4/9.
     
  2. jcsd
  3. Nov 4, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Hiche! :smile:

    Yes, 4/9.

    Probably best to specifically say that Z ≥ 3 means that there is no 3 or 4 in the first two rolls, the probability of which is P(not A or B) squared. :wink:
     
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