2. (Probability spaces) (a) Let (QC, P) be a probability space. Let A be an event in the collection .7, such that P(A) 7E 0, on which we want to condition. We dene a collection of events .FA as the collection of the intersection of A with all the events in .F: J"A={AF:FE.7-"}. If we consider a new sample space (2A 2: A, prove that 3% is a valid collection, and also that the conditional probability measure P(SA) PA(SnA):= P(A) , (1) where S E .7, is a valid probability measure on .754