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Topic: Tennis Set (Read 628 times) |
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ThudnBlunder
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Every week young Pete plays his grandpa at tennis, each winning exactly half of the matches. When they are both fresh his grandpa is the better player, but he tires rapidly so that his probability of winning the nth set is pn, where p is the probability that he wins the first set. If they always play best-of-5 matches, find the value of p.
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| « Last Edit: Jan 24th, 2005, 3:08pm by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Noke Lieu
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Re: Tennis Set
« Reply #1 on: Jan 24th, 2005, 3:36pm » |
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on Jan 24th, 2005, 3:06pm, THUDandBLUNDER wrote: each winning exactly half of the matches.... they always play best-of-5 matches,
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How's that work then? surely eaier to say they always play five matches?
Gp,Gp,draw,Pg,Pg....
And tennis matches can't be drawn- tie breakers. I realise that these are maths games of tennis that can be.. so I won't elaborate on it. Maybe a bit of confusion (my end) on difference between sets and matches?
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rmsgrey
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Re: Tennis Set
« Reply #2 on: Jan 24th, 2005, 3:55pm » |
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on Jan 24th, 2005, 3:36pm, Noke Lieu wrote:| How's that work then? surely eaier to say they always play five matches? |
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My interpretation was that each match is best-of-5 sets, and, over many weeks, the match wins average at 50-50
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Eigenray
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Re: Tennis Set
« Reply #3 on: Jan 24th, 2005, 8:47pm » |
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p=0.777861...
...Easy?
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towr
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Re: Tennis Set
« Reply #4 on: Jan 25th, 2005, 1:02am » |
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I get an ever so slightly different answer, but that may well be down to program-inaccuracy.. :: 0.77730704776...::
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| « Last Edit: Jan 25th, 2005, 1:02am by towr » |
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Grimbal
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Re: Tennis Set
« Reply #5 on: Jan 25th, 2005, 3:14am » |
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I get p=::0.7778614934981::
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towr
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Re: Tennis Set
« Reply #6 on: Jan 25th, 2005, 6:11am » |
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Anyone got any got tips for free (not pirated) calculator/algebra programs? Cause my current one doesn't seem up to the task. 
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Grimbal
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Re: Tennis Set
« Reply #7 on: Jan 25th, 2005, 8:47am » |
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For every error for which we blame the computer, there are at least 2 human errors. On of the errors being to blame the computer.
No frankly, are you sure you fed the right equation into your program?
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Barukh
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Re: Tennis Set
« Reply #8 on: Jan 25th, 2005, 8:59am » |
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on Jan 25th, 2005, 8:47am, Grimbal wrote:| No frankly, are you sure you fed the right equation into your program? |
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Are you sure Eigenray also used the computer?!
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Eigenray
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Re: Tennis Set
« Reply #9 on: Jan 25th, 2005, 2:06pm » |
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If the intended solution is to tell a computer to solve f(0)+f'(0)+f''(0)/2=1/2, where f(t) = product[pk+t(1-pk), k=1..5], then I guess it's easy.
When I see a problem along the lines of "find p such that...", I spend a while trying to do it by hand, and only resort to a computer when it's clear I can't get it in any nicer form. If I have a polynomial of degree 15, and no obvious substitutions to simplify it, then either the puzzle just wants a numerical approximation, or it's probably not "easy". I often get disappointed if it's the former.
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