8. Show that conditional probability defines a valid probability measure on the sample space S. That is, let B denote any event with P(B) > 0. Show that the following three statements hold. Statement 1. For every event A, P(A|B) 2 0. Statement 2. P(S|B) = 1. Statement 3. For disjoint events A1, A2, ..., P(UA;|B) = >P(A;|B). (Hint: For Statement 3, you might want to draw a picture so you can see how unions and intersections "distribute." )