Given 3 red balls of value 3, 2 blue balls of value 5, and 1 yellow ball of value 25
a) What is the expectation for X of drawing two balls? Where X is the value.
My issue here is that we have no way to be sure what ball was drawn the first time, I have calculated the X of drawing one ball to be 7.33.. So at first I thought I might subtract this off my answer to simulate that much value being "lost" because it couldn't be drawn again. But that doesn't make much sense, so I am not sure how to proceed.
b) Suppose you are allowed to keep drawing balls until you draw the yellow ball. (So you will draw at most six times, since the balls are not replaced after each draw.) What is the expectation for X of balls drawn?
I know how to do this problem in regards to dice, but again, the lack of replacement is giving me trouble.