Question 234454
Since the original estate was assumed to be divided by 2, and we are now dividing by 3, then each person's share needs to be multiplied by 2/3 to make it equal.


The wrinkle is what the wife gets.


She will have to get 2/3 times the average of what she would have gotten had the son been born or had the daughter been born.


Here's how it works out:


son gets 2/3 * 2/3 = 4/9
daughter gets 2/3 * 1/3 = 2/9
wife gets 2/3 * (1/3 + 2/3)/2 = 3/9


4/9 + 2/9 + 3/9 = 9/9 = 1 so the total is intact.


They are all either very happy or very unhappy, depending more on circumstances not having to do with whether the sharing was equitable or not.


If you consider the laws of probability and if you assume the probability of getting a boy or a girl was even, then the wife had a .5 probability of the child being a boy and a .5 probability of the child being a girl.


This means that 50% of the time, she would have made 2/3 of the estate and 50% of the time she would have made 1/3 of the estate.  Her expected value over the long term would have been .5 * 2/3 + .5 * 1/3 = 1/2.


This means that the averaging of what she would have gotten had it been a boy with what she would have gotten had it been a girl, was an equitable solution.  


Answer is, in my opinion,


boy gets 4/9
girl gets 2/9
wife gets 3/9


of the estate.