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February 13

linear programming

When setting up constrains when using the simplex method can you use two equations for the same variable such as A=>B and A<=C in order to achieve an overall constrain that is a value between B and C? 71.100.8.16 (talk) 00:22, 13 February 2010 (UTC)[reply]

If B and C are also variables you'd set it up as B-A<=0, A-C<=0. Or introducing slack variables, B-A+X=0, A-C+Y=0.--RDBury (talk) 06:19, 13 February 2010 (UTC)[reply]

Lottery

Sorry if this is a stupid question, I'm not good at statistics:

Situation A:

1000 people each buy a lottery ticket for draw # 1

Situation B:

100 people each buy a lottery ticket for draw # 1; 100 other people each buy a lottery ticket for draw # 2; 100 other people each buy a lottery ticket for draw # 3; and so on for a total of 10 draws.

Is the probability that someone will win a prize equal in both situations? Poolofwater (talk) 15:54, 13 February 2010 (UTC)[reply]

That's going to depend on the rules of the lottery. How are winners selected and what prizes are there? --Tango (talk) 15:55, 13 February 2010 (UTC)[reply]

If the tickets are chosen at random yes. E.g. in theory someone in each of the 100 could win, so they win ten prizes. But also in theory the people in situation A could buy ten tickets with the same number that win. The chance might be vanishingly small in each case though.

If it's one person buying all the tickets then one way to increase your chance of winning a prize is but tickets with different numbers. E.g. if each draw has only 1000 numbers you can buy all 1000 in situation A and so guarantee a prize. In situation B you could still lose each draw. Of course real lotteries tend to have have much longer odds than 1 in 1000, so even if you bought your tickets at random they would likely all be different so the odds would be almost the same. And this is just your chance of winning something. Your expected winnings are the same whether you choose tickets at random or not.--JohnBlackburne^words_deeds 15:57, 13 February 2010 (UTC)[reply]

Thanks very much! Poolofwater (talk) 16:05, 13 February 2010 (UTC)[reply]