Please do these two things when solving the problem:

i) Use words to describe the solution process

ii) If you use a theorem or proposition, please state what it is called and your source. For example, THEOREM 3.1, ROSS, CHP 3.

1. Let S be the unit square in the plane; and, for any subset E of S, let (E) be the area of
r.
(a) Is f a probability on S? Why or why not'? (Hint: check the axioms).

(b) If f were a probability (or if it, is a probability). what is the value of PA Iff)7. What is the value of (GII K)?

Note: K is the tall skinny rectangle on the left, CY is the upper left triangle. F is the lower right triangle, and Ii is the lower half of the square. See the tgram below.

c) which of the sets in the diagram below are independent?why or why not?(be sure you get all pairs of sets)