Products and expectation values

Let us start with an instructive example (modified from one I learned from Steven Landsburg). Let us play a game:

I show you three identical looking boxes. In the first box there are 3 red marbles and 1 blue one. In the second box there are 2 red marbles and 1 blue one. In the last box there is 1 red marble and 4 blue ones. You choose one at random. What is …

• The expected number of red marbles you will find?
• The expected number of blue marbles you will find?
• The expected number of marbles, irregardless of colour, you will find?
• The expected percentage of red marbles you will find?
• The expected percentage of blue marbles you will find?

Answer below the cut…