It's important to distinquish between the method, and the domain. In this case we have the method of linear programming, which is being applied to the probability domain.
So it isn't a question (per se) about probability, rather about formulating a linear programming problem. The probability domain simply provides some of the constraints used to solve the problem.
Also in your example, the question implies perfect measurement of uniquely distinguished results, so if they say that a 5 was rolled on the dice, then you can be certain, however if they say the tree was 5m tall (and to have say a distribution listing 4.95m, 5.0m, 5.05m) you could expect that it was simply round off... a much more tricky problem..
For this simple single sample example, the likelihood of one distribution to the other is the ration of the individual distribution probabilities (because most of the possibles are multiplied by zero, the number of samples with that value).
When you have multiple results in the sample, you get a 'proper' linear programme, again multiplying out the number of occurences by the probabilities in the individual distributions, and then comparing the overall numbers (usually with a little differentiation...)
Philip Oakley
