A jar contains nine blue marbles numbered 1 through 9 and six red marbles numbered 1 through 6. You reach into the jar and select a marble at random out of all the marbles that are in it. You select 3 marbles at random from the jar. Given that two of these marbles are blue and one is red, what is the (conditional) expectation of the sum of the numbers on these marbles?
I'm not sure how to do conditional expectation. I feel like I would need to find the probability of each sum but I'm not sure. Any help would be appreciated. Thanks!
Hint: If there are two blue and one red, the expected sum is the expected sum of the blues plus the expected "sum" of the red.