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Probability in a die

  1. Sep 29, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppose we have a biased three sided die. When trying to calculate the probability of rolling a number, we find that half of the time we're accurate, and the other half of the time we observe a random number 1 through 3 (uniformly distributed). I've calculated the probability distribution of observing a given number as [itex] \rho = \begin{pmatrix} p_1 \\ p_2 \\ p_3 \end{pmatrix} [/itex]. That is, the probability of rolling "i" is [itex] p_i, i=1,2,3 [/itex]. Now let's say that in an experiment I throw the three sided die, and a "1" appears. I need to write down the probabilistic state describing my knowledge of how the die lies after the observation.


    2. Relevant equations

    Perhaps Baye's law on conditional probability
    [tex] P(a|b) = \frac{P(b|a)P(a)}{P(b)} [/tex]

    3. The attempt at a solution

    I would imagine this is a one-liner, but I can't quite figure out how to do it.
     
  2. jcsd
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