Mathematics Help to calculate the probabilities!, challenging question
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 Jul 14 2009, 11:28 PM, updated 17y ago
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#1
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Junior Member
10 posts Joined: Jul 2008 
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There are 15 pigs are racing and they are wearing the number from 1-15 respectively. Here are 5 strong pigs are categorized as favorite, they are number 2, 6, 9, 10 and 12. The question is: calculate the probabilities to get an odd and even for the sum of number of champion, 1st runner-up and 2nd runner-up. Example, champion=number 6, 1st runner-up=9 and 2nd runner-up=1, then the sum=16, then 16 is even.
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Jul 15 2009, 10:49 AM
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#2
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10 posts Joined: Jul 2008
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QUOTE(Thinkingfox @ Jul 15 2009, 12:16 AM) I think at least one additional information is required. You say there are favourites, so what is the additional probability for a favourite pig to win compared to an ordinary pig? Those favoured are not necessarily to get into top 3. The top 3 may be all non-favoured, also can be all favoured, of course can be 2 favoured and 1 non-favoured, 1 favoured and 2 non-favoured. The highest prob for a favourite pig to win also can be out of top 3 and at the same time other favourite pigs get into top 3. So, is there the probability for favourite pig to win still needed?   |
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Jul 15 2009, 01:11 PM
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#3
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QUOTE(bgeh @ Jul 15 2009, 11:54 AM) Yes you need to, else it'll be a 15-variable problem which would be a pain in the arse (algebraically) to solve like tat ah...then let say pig number 9 got 30% chance to get into top 3, number 2 and 10 20% respectively, number 6 and 12 15% respectively. how can it gonna to be solved? any idea to start the calculation? This post has been edited by darkwall: Jul 15 2009, 01:23 PM |
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Jul 15 2009, 01:29 PM
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#4
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QUOTE(bgeh @ Jul 15 2009, 01:20 PM) I'll provide the steps: there are 455 combinations Firstly get all the listed probabilities of the pigs to win Secondly, to simplify the calculation, we assume indepedence of each pig's performance in the race to all its contemporaries. Compute the probabilities of every possible combination that gives you either an even or odd number (which will be very very very long) do we nid the permutation? if yes, 2730 combinations |
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Jul 15 2009, 01:37 PM
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#5
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QUOTE(ahjames @ Jul 15 2009, 01:34 PM) why use pigs? actually i'm thinking to use kangaroo... why cant use horse?  |
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Jul 16 2009, 11:15 AM
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#6
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QUOTE(Thinkingfox @ Jul 15 2009, 08:54 PM) So, you're saying that a favourite pig has an equal chance to an ordinary pig? i.e. it's favourite not because of it's high chances of winning. nope. its favourite because of it's higher chance to win if compare to others. |
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Jul 17 2009, 07:00 PM
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#7
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QUOTE(Thinkingfox @ Jul 16 2009, 06:15 PM) So what is the probability of a favourite pig compared to an ordinary pig? only provide the prob is higher for fav pigs if compare to other pigs, no exact number. |
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