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. k P(X = k) 1 2 3 4

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