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#1
08-09-2007, 02:12 PM
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A Talmudic expectancy question
An interesting expectancy question came up today when studying a section in the Talmud. Maybe someone here can calculate the numbers for me.
Background first: By Jewish law if a guy dies without kids then his brother must marry the widow or perform what is know as "Halitza" which is a sort of divorce ceremony. Until he does this she is not permitted to marry anyone else. If he does the Halitza she may then marry anyone else EXCEPT for him. So, the following weird case was discussed. We have 5 unrelated guys each of whom has a brother. However, though we know who all the 5 brothers are, we do not know which one is the brother of which. The first 5 guys all die. How do we solve the problem so that all the widows can get married? The Talmud gives 2 possible solutions: 1. Each of the guys will do "Haliza" to 4 of the widows and marry a fifth. Obviously, each widow marries one guy. In this way all the widows are married to a guy. Each of the widows is married to the correct guy or has performed "Haliza" to him and was therefore free to marry anyone. 2. 4 of the guys do "Haliza" to all 5 widows and one guy marries them all. [img]/images/graemlins/smile.gif[/img] In this way we are guaranteed that at least one of the widows has married the correct guy. Since it is considered better to marry rather than perform "Haliza" this might seem to be a better solution. So, now to the question. In case 2 it is obvious that the expectancy of "correctly married" women is 1. What would it be in case 1? It is possible that none would be correct. It is also possible that all would be correct. How do I calculate this? 
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#2
08-09-2007, 04:57 PM
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Re: A Talmudic expectancy question
Is this another one of those deals where we answer a simple question and get a free bible?
The questions are usually easier than this.
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#4
08-09-2007, 05:53 PM
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Re: A Talmudic expectancy question
[ QUOTE ]
An interesting expectancy question came up today when studying a section in the Talmud. Maybe someone here can calculate the numbers for me. Background first: By Jewish law if a guy dies without kids then his brother must marry the widow or perform what is know as "Halitza" which is a sort of divorce ceremony. Until he does this she is not permitted to marry anyone else. If he does the Halitza she may then marry anyone else EXCEPT for him. So, the following weird case was discussed. We have 5 unrelated guys each of whom has a brother. However, though we know who all the 5 brothers are, we do not know which one is the brother of which. The first 5 guys all die. How do we solve the problem so that all the widows can get married? The Talmud gives 2 possible solutions: 1. Each of the guys will do "Haliza" to 4 of the widows and marry a fifth. Obviously, each widow marries one guy. In this way all the widows are married to a guy. Each of the widows is married to the correct guy or has performed "Haliza" to him and was therefore free to marry anyone. 2. 4 of the guys do "Haliza" to all 5 widows and one guy marries them all. [img]/images/graemlins/smile.gif[/img] In this way we are guaranteed that at least one of the widows has married the correct guy. Since it is considered better to marry rather than perform "Haliza" this might seem to be a better solution. So, now to the question. In case 2 it is obvious that the expectancy of "correctly married" women is 1. What would it be in case 1? It is possible that none would be correct. It is also possible that all would be correct. How do I calculate this? [/ QUOTE ] The probability that each woman marries correctly is 1/5, so the expected value is simply the sum of these probabilities or 1.
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#5
08-09-2007, 07:38 PM
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Re: A Talmudic expectancy question
[ QUOTE ]
The probability that each woman marries correctly is 1/5, so the expected value is simply the sum of these probabilities or 1. [/ QUOTE ] Makes sense. So, in fact, the two options give the same result.
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#6
08-10-2007, 05:02 PM
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Re: A Talmudic expectancy question
[ QUOTE ]
[ QUOTE ] The probability that each woman marries correctly is 1/5, so the expected value is simply the sum of these probabilities or 1. [/ QUOTE ] Makes sense. So, in fact, the two options give the same result. [/ QUOTE ] Actually, you're going to have to be a lot more clear about what a "correct" marriage is. Your methodology seems to assume that there is one uniquely correct man for each woman, and vice versa. It also assumes that the men and women themselves can't figure this out on their own. However, if we assume that the men and women would pair off at random, and that all "incorrect" marriages are equally valueless, then the average results would be the same: 1 correct marriage and 4 incorrect marriages.
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#7
08-16-2007, 08:05 AM
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Re: A Talmudic expectancy question
[ QUOTE ]
Actually, you're going to have to be a lot more clear about what a "correct" marriage is. [/ QUOTE ] The definition of "correct" is marrying the late brother's wife.
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