(A recursively defined probability experiment) A probability experiment proceeds in steps as follows

(we care about the ordering of the steps):

Step 1: Pick a real number.

Step 2: If the real number was negative, then stop the experiment. Else, go to step 1. a) Give a precise mathematical description of a set S that acts as the sample space. You must consider the

possibility that the experiment never ends. What is |S|? b) Modify Step 1 by picking a number in the set {1,1}, rather than picking a real number. Under this

modification, what is S and |S|? c) Modify Step 1 by picking a number in the set {1, 1}, but also excluding the possibility that the experiment

never ends. Under this modification, what is S and |S|?