# Probability of multiple classification results being incorrect

I am running an image classification with 5 classes. There is a large set of training data from which I randomly select a training subset, yielding slightly different classifications. I run the classification three times, and obtain the following user's accuracies for each class (the user's accuracy is the probability that a certain pixel of a given class is correctly classified):

1 | .794 | .802 | .796
2 | .511 | .506 | .503
3 | .938 | .941 | .940
4 | .909 | .907 | .912
5 | .768 | .765 | .765

For each pixel, there are three outcomes:

1) All runs have the same class (either none are wrong or all are wrongly classified)
2) 2 runs have the same class (either 1, 2 or all were wrongly classified)
3) All runs are different (either 2 or all were wrongly classified)

I would like to calculate the probability for each combination of results, of each of these outcomes:

1, 1, 1: P none wrong, P all wrong
1, 1, 2: P 1 one wrong, P 2 wrong, P all wrong
1, 2, 3: P 2 wrong, P all wrong
etc...

I'm not sure how to approach the problem? Could any one lead me in the right direction? Is it simpler to assume that the accuracies are the same for each run?

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Seems like you would use the multinomial distribution. – PEV Dec 18 '10 at 3:47
For example, (1,1,1) and (5,5,5) correspond to outcome 1. – PEV Dec 18 '10 at 3:53