Amount of outcomes in a tree diagram If I have 2 red marbles and one blue marble, and I take one out of a bag 2 times, but I  put them all back in after taking one out, how many outcomes are there. I am not sure if for example the combination of the blue marble with any of the two red marbles should be seen as 2 or 1 outcome because this determines if there are 4 or 9 overall outcomes. Please help, because I have been told that it should be 9 but according to me the 2 red marbles are exactly the same?
 A: If you want all branches of the tree to have the same probability, then you have to treat the two red marbles as distinct, so that you get the $3^2=9$ outcomes $R_1R_1$, $R_1R_2$, $R_1B$, $R_2R_1$, $R_2R_2$, $R_2B$, $BR_1$, $BR_2$, and $BB$. There are two different red balls, whether you can tell them apart or not, so there really are these nine different outcomes, all of which are equally likely.
You can also make a tree diagram based strictly on the sequence of colors that you see when you draw the two marbles; it will have just four branches, one for each of the outcomes $RR$, $RB$, $BR$, and $BB$. However, these outcomes will no longer be equally likely: on each draw you’re twice as likely to get $R$ as to get $B$. You can reflect this fact in the tree by labelling each edge with the appropriate probability:
                                     *  
                                    / \  
                                   /   \  
                             2/3  /     \  1/3  
                                 /       \  
                                /         \
                               R           B  
                              / \ 1/3     / \  
                        2/3  /   \   2/3 /   \  1/3
                            /     \     /     \  
                           RR     RB   BR     BB  
                          4/9    2/9   2/9    1/9

The probabilities of the final outcome at the end of a branch is then calculated by multiplying together the probabilities that appear along that branch.
