' , 7 Alice draws a number X N Geom(p), 0 0. Alice Wins if her number is larger than Bob's. Find the range of p as a function of A such that the probability Alice Wins is greater than or equal to 0.5, that is, P{X > Y} 2 0.5. (Hint: You will need to use formulas for the geometric sum and the Maclaurin series for em.)