5 (Un conditional (In )equalities Let us consider a sample space 2 = {@1, ..., @w} of size N > 2, and two probability functions P1 and P2 on it. That is, we have two probability spaces: (2, P, ) and (2, P2). (a) If for every subset A C 2 of size A = 2 and every outcome w E 2 it is true that PI (@ | A) = P2 (@ | A), then is it necessarily true that Pi (@) = P2 (@) for all w E ? That is, if P, and P2 are equal conditional on events of size 2, are they equal unconditionally? (Hint: Remember that probabilities must add up to 1.)