341I think that and the concept of Catalan Numbers does the trick. we seem to need to ignore the number of ways climbing the grid without ever going above the line y = x and that smacks of Catalan numbers.
2 candidates contested for an election, A & B. A got a votes, while B got b. Given a>b, find probability that A was ahead of B - throughout the competition..... SHOULD IT NOT BE JUST 12??????????????
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11 Answers
62no Soumik I don't think it should be 1/2
simply because it should depend on a and b.
like take the case wehn B got zero votes. the probability is 1!
62I think the best way to solve it would be through a axb grid...
What do you guys think?
34162One thing that is most commendable about prophet sir is that he knows the names of every trick under the sun :D
I din know that this was somethign related to Catalan number or infact it existed even though i have used this trick several times !!
341i am not very familiar with it, but it did remind of that concept. Lets see
62http://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem
Read this one..
Even i read catalan numbers last month..
I thought that this could be pulled off by recursion but now it seems unlikely....
see the proof on the page.. and the solution
btw I wont be here for 2 days.. bye till then [1]
3the no of votes that A has more than B=a-b
so the probability that A can lead the election =a-b/a+b.
i hope this is rong,due to the above discussion,i just want to know why i am rong.
62I dont get the logic sankara.. I mean how is it obvious to you.. to me it is not at all obvious!