Let us consider a sample space = {1,...,N} of size N > 2 and two probability functions P1 and P2 on it. That is, we have two probability spaces: (,P1) and (,P2). CS 70, Summer 2021, HW 4 2 (a) Suppose that for every subset A of size |A| = 2 and for every outcome , it is true that P1 ( | A) = P2 ( | A). Is it necessarily true that P1 () = P2 () for all ? That is, if P1 and P2 are equal conditional on events of size 2, are they equal unconditionally? (Hint: Remember that probabilities must add up to 1.)