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This problem can be solved by using Negative Binomial distribution NB(r,p), where the r is the number of success(boys), in this case: r=1. Let X be the number of girls. You would need to calculate the expected value of girls: E(X)= pr/(1-p)=(1/2)/(1/2)=1 for NB distribution. So the ratio is E(X)/E(# of boys) = 1/1=1.
- xuan.liu113 March 27, 2014This question can be extended: say the probability of having a boy is not 1/2, say 51/100, and # of boys each family want is 3. Now this ratio should be E(X)/r = p/(1-p) = 49/51. So the # of boys won't affect the ratio, while the probability of having a boy will.