Given two urns, one containing two red, three green, and four yellow balls, and the other containing four red, two green, and three yellow balls, if a single ball is drawn from each urn, what is the probability that: 16. Both are red?
At least one is green?
One is red, the other yellow?
At least one is either red or yellow?
Now imagine that you are going to draw a ball from one of the urns, but which one you draw from will be randomly determined by a roll of a six-sided die. If the die comes up 1, you will draw from the second urn; otherwise you will draw from the first. You won't be able to see which of the two you drew from. If you drew a red ball, what is the probability that you drew from the first urn?