SOLUTION: Al-Kwarizmi's will was drawn up when he was near death, and his wife was expecting their first child. in his will, he stipulated that if his wife were to have a son he would inheri

Question 234454: Al-Kwarizmi's will was drawn up when he was near death, and his wife was expecting their first child. in his will, he stipulated that if his wife were to have a son he would inherit two-thirds of his estate and his wife the remaining one-third. if his wife was to have a daughter she would receive one-third and the wife two-thirds of his estate. as it turned out his wife had twins a boy and girl.
How should the inheritance have been divided among his wife, his son, and his daughter so that al-Kwarizmi's wishes were respected?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
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