Again refer to the game of darts explained in Example 1.2.7. (a) Derive the general formula for

Question:

Again refer to the game of darts explained in Example 1.2.7.
(a) Derive the general formula for the probability of scoring i points.
(b) Show that P(scoring i points) is a decreasing function of i, that is, as the points increase, the probability of scoring them decreases.
(c) Show that P(scoring i points) is a probability function according to the Kolmogorov Axioms.