A more colorful roll of the Dice
I have a pair of special 6-sided dice. One of them has 3 Red sides, 2 Yellow sides, and 1 Blue side. The other has 2 Red sides, 3 Yellow sides, and 1 Blue side. Assume the dice are fair (probability of rolling any face = 1/6).
I pick them up, shake them in my hand, and then roll one. If it shows blue, I ignore that roll, pick it up and start over. If it is not, I will roll the second. On average, what is the probability that I will roll at least one red or yellow, but not both?