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[quote=Anonymous]No need to feel bad, this is really complicated.  I think pp explained it pretty well, but maybe I can make it a little more simple.

Two schools.  1 spot in each.  2 applicants for A.  10 for B.  Same number of applicants for each school regardless of the type of lottery.

You can only get into one school.  This is true in either lottery, as your child will end up only attending one school.  In the multiple lottery system, you could have gotten into more schools at first and held them, but eventually you would have to prioritize and make a decision on one school, thus freeing up the space for others.  In the new system, you prioritize beforehand, so you only get into one school at the beginning and the other spots, which are less desired by you, are instantly freed up.

Imagine a 10 sided die.  For school A, you only have a 1 in 10 shot, therefore, you must roll a 1 to get into school A.  For school 2, you have a 1 in 2 (or 5 in 10) chance.  Therefore, you must roll a 5,6,7,8,or 9 to get into school B.  (It could be any 1 number and any 5 numbers, but the five numbers of B cannot contain the 1 number of A because that would mean that you would be in more than one school).

If different lotteries, you would roll 1 time for school A, and you would have a 1 in 10 chance of getting a 1.  You would then roll 1 time for school B, and you would have a 5 in 10 chance of getting school B.  Thus, in total, you would have 6 in 10 chance of getting into one of the schools.

If one lottery, you would roll 1 time.  If you rolled a 1, you would get school A; if you rolled a 6,7,8,9, or 10, you would get school B.  You would therefore have a 6 out of 10 chance to get into 1 of the schools.

Does that make sense?
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