A four digit number is formed by randomly drawing four numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, with replacement. The digits are written down in the order they are drawn. (Note: In this problem, we will not consider numbers beginning with 0 to be four digit numbers. If 0 is drawn first, it is replaced, and we randomly draw again, until we get a number that is not 0).

We will define the following events:

A = the four digit number is even.

B = the four digit number is divisible by 4.

C = the four digit number is divisible by 5.

Find:

a) P(A), P(B), P(C)

b) P(B U C)