boys and girls I feel the posted solution is wrong. The probaility of success, ie. probability of getting a boy, is p = 1/2. The probability of egtting a girl is q = 1/2. Lets say X is the random variable tht represents the number of births before we get a baby boy. The expected value of this variable is E[X} = sum_{k=1 to infinity} K * q^(k-1) * p which is equivalent to  (p/q) * sum_{k=0 to infinity} k * q^k. On evaluation this turns out to be 1/p which means 2. That means, it takes on average, 2 births before we get a baby boy. That is 2 girls born on average for every boy. The ratio and the answer, thus, is the ratio of girls to boys is 2:1 Mitesh Vasa Friday, July 9, 2004 Your math is right, your interpretations is not. "2 births before we get a baby boy" means that on average you get a boy on the SECOND attempt. Which means that you have a single girl before you get a boy. So the ratio is 1:1. Brad Corbin Saturday, July 10, 2004 i think the solution is wrong ... here's mine ... the no. of boys for a couple is 1. the expected no. of girls can be calculated as ... N(g) = 0*0.5 + 1*0.25 + 2*0.125 + 3*0.0625 + .....       = 2/3. so the ratio of boys to girls is 3/2 Ram Saturday, July 31, 2004 The expected proportion of boys, even for a finite number of babies, is exactly 1/2. The proof is easy if you step back a bit from the infinite sum and conditional math [which do work but requires effort!]  Each baby is a boy or girl with 50% probability by definition. No baby's sex influences any other baby's sex, so every born child had that same 50% chance. So for any group of babies, no matter what crazy rules you make to decide who has them and why and how many, the proportion is still 1/2. Steve W Friday, September 17, 2004   Fog Creek Home