1. The problem statement, all variables and given/known data You start out with a bag that contains either a red marble or a green marble with equal probability. Then, a red marble is added to the bag. If I draw out a red marble the first time, what is the probability of drawing out a green marble the second time? 2. Relevant equations 3. The attempt at a solution So, we know that P(R) = P(G) = 1/2, which implies that P(RR) = P(RG) = 1/2. I drew a decision tree / \ RG RR / \ / \ G R R R (the leaves correspond to the marbles left in the bag) and it seems like the probability that I draw out a green marble the second time is 1 / 3 (because there are 3 ways in which I can draw out a red marble, and only one of those ways correspond to me drawing out a green marble). I'm not quite sure if this is the correct solution, because the two red marbles that might be in the bag would be indistinguishable, so I'm not really sure how it would affect the overall probability space. I also tried calculating P(G | R) as follows. P(G | R) = P(G and R) / P(R). At first, I computed P(G and R) as 1/2, but I think counting the scenario where I draw out a green marble first and then I draw out a red marble might be overcounting the number of outcomes. P(R) is just 3/4.