Help - where to start expected value of random variable problem?

Question

Find the expected value of the random variable in the experiment:
A bag contains six marbles, of which four are red and two are blue. Suppose two marbles are chosen at random and X represents the number of red marbles in the sample.

Answer 1

If you repeat this experiment a thousand times or a million times, 2/3 of all the marbles you pull out will be red. Since you pull out two marbles in each experiment, 2/3 of 2, or 4/3 is your expected value of X.

Conversely, on the average, you'll pull out 1/3 x 2 = 2/3 blue marbles. Notice that 4/3 + 2/3 = 2 marbles.

Another way to look at it is that you'll pull twice as many red marbles as blue marbles. A 2-to-1 ratio for 2 marbles also gives you the 4/3 and 2/3 split.