You are rolling a die. One face of the die is painted green, another red, and the rest of the faces are black. Find the probabilities of the following events.

(a) In the first three rolls, the die lands with black faces up, and in the next two with green faces up.

(b) In five rolls, the die shows a black face exactly 3 times, and a green face two times. Realize the difference between this question and the previous.

(c) The die will show a black face for the first time in the sixth roll.

(d) The die will show a black face after the fifth roll. Realize the difference between this question and the previous.

(e) There will be either green or red faces in the first five rolls.

(f) The first run of one color of a length of 3 will happen in the fifth roll.