1. This color circle above is comprised of the three primary(P), three secondary(S), and six tertiary(T) colors. Imagine that there is a spinner in the center of the circle that, when spun, has an equal likelihood of stopping in any of the twelve colors(defined here clockwise as purple(S), deep blue(T), blue(P), teal(T), green(S), spring green(T), yellow(P), chartreuse(T), orange(S), rose(T), red(P), and violet(T)). When the spinner stops, we assign 3 points if on a primary color, 2 points if on a secondary color, and 1 point if on a tertiary color.

a) What is the expected value(mean) of a single spin?

b) What is the variance?

c) If the spinner is spun four times, what is the probability that the total score is at least 10 points?

d) There is a 6% probability that the spinner falls exactly on the line between two colors(hint: there are twelve lines between colors). If this occurs, points are given for the colors on both sides of the line(add the points for the two colors).

e) With the above rule added, now what is the probability that the total score of four spins is at least 10 points?