# Mutual Information from confusion matrix with conditional marginals

I have a table that looks like this

  --Predicted --------------------
Blue    | 0.15 | 0.25  | 0.4
Green   | 0.15 | 0.475 | 0.2
Red     | 0.7  | 0.275 | 0.4
| Red  | Green | Blue
----  Actual --------


The sum of each column is equal to one. They are actually the conditional probabilities, for example the probability to predict a red when the actual was red is 70%. Similarly, the probability to predict a blue when the actual one was green was 25%, etc...

How do I calculate the mutual information for this table please? I dont think that is possible with only these numbers above, i need the counts in each cell I believe, is that right? For example, how are you going to calc the prob that a ball has a real/actual color of red? Thanks!

If you only have the conditional probabilities $$p(x|y)$$ where $$x$$ is the predicted and $$y$$ the actual, you will also need the probability $$p(y)$$ of the actual. This way you can compute $$p(x, y) = p(x|y) \cdot p(y)$$ and from that you can get the MI.