Two children play a game where one child randomly selects three toys without replacement, from a box containing eleven action figures (5 batman, 3 spiderman, 3 wonder woman). She gives away one piece of candy every time she selects a batman, and gets one piece of candy every time she selects a wonder woman. Define X as the total pieces of candy she earns (where earns = wins/loses). S = event that she chooses a spiderman B = event that she chooses a batman W = event that she chooses a wonder woman a) What is the sample space of X? b) What is the PMF of X? c) Show that your PMF is a valid PMF.