An urn contains 10 red, black, and green balls. One of the colors is chosen at random (meaning that the chosen color is equally likely to be any of the colors), and then balls are randomly chosen from the urn. Let X be the number of these balls that are of the chosen color.

a. Find P(X = 0).

b. Let X_i equal 1 if the i^th ball selected is of the chosen color, and let it equal otherwise. Find P(X_i = 1), i = 1, 2, 3, 4.

c. Find E[X].