So, as I have understood it, if you have two experiments and you want to know the probability of a set of two outcomes happening concurrently, then you multiply the chance of the first outcome by the chance of the second outcome and voila, you have your probability.
However, I am confused as to when this doesn't work. For example, I just did a problem:
James lives in San Francisco and works in Mountain View. In the morning, he has 3 transportation options (bus, cab, or train) to work, and in the evening he has the same 3 choices for his trip home. What is the probability that he uses the same of mode of transportation twice?
My first inclination was 1/9th but apparently I am wrong. I was told to use a tree to count the favorable outcomes. I did so, and see that the answer is 1/3, but for the life of me I can't see the difference between this question and the first type I mentioned.
I am obviously missing some finer points or nuance in the question which should clue me in. What is it?