2. [-/1.25 Points] DETAILS UHSTAT4 8.E.021. MY NOTES PRACTICE ANOTHER A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth. (a) The simple events in the simple space are {G, BG, BBG, BBBG, BBBB}, where we use B for boy and G for girl. For instance, one simple event is BG, because the woman quits once she has a girl. Find the probability for each of the simple events in the sample space. P(G) = P(BG) = P(BBG) = P(BBBG) = P(BBBB) = (b) Find the probability distribution function for X. + m N X P(X = k)