Covariance question

[T.H.]

Okay so lets take two securities A and B. Normally they would have probabilities along the lines of 0.25 good 0.5 mediocre 0.25 bad and E[r] of 12 and 6. That's pretty straightforward. I stumbled upon a question that gives separate probabilities for each asset. So for asset A 0.25 good 0.5 med 0.25 bad and for asset B 0.33 good 0.33 med 0.33 bad. E[r] would be the same as above. How do you approach calculating the co variance when the probabilities for each asset are different ? I tried averaging the probabilities out and the covariances I got were very low which would be in line with what the full question indicated but I am not really confident in my answer. Anyone have any ideas on how to approach this ?