An urn contains 5 red, 7 green, and 8 blue balls. Three times in a row, we pick a random ball (uniformly) from the urn and then a) replace or b) not replace it.
If the first two balls have the same color, what is the probability that the third ball also has the same color?
What is the probability of this scenario for with replacement or without replacement. I am confused on this one as I tried just summing the probabilities and I got 100% for without replacement which is obviously not right. I think it has something to do with conditional probability, but I'm confused as to how I would use that.