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Author Topic: TPIR math problem  (Read 2984 times)

toetyper

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TPIR math problem
« on: August 13, 2008, 04:42:08 PM »
in the game switCheroo.  Whats the probability of getting all 5 prizes wrong on BOTH tries assuming

the numbers are placed randomly

on the second try none of the  numbers are in the same place
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parliboy

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TPIR math problem
« Reply #1 on: August 13, 2008, 05:00:58 PM »
[quote name=\'toetyper\' post=\'193919\' date=\'Aug 13 2008, 03:42 PM\'] in the game switCheroo.  Whats the probability of getting all 5 prizes wrong on BOTH tries assuming

the numbers are placed randomly

on the second try none of the  numbers are in the same place [/quote]

My non-mathematician's guess:
For the first attempt: 32.7%
For the second attempt: 23.7%
For both attempts: 7.5%
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Speedy G

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TPIR math problem
« Reply #2 on: August 13, 2008, 10:28:40 PM »
Working through a couple of simpler cases to help with counting, I come up with 44 arrangements where no numbers are right.  (Also, 45 with 1 number right, 20 with 2 numbers right, 10 with 3 numbers right, and the 1 with 5 numbers right, for a total of 120 possible arrangements)  That's 36.6 (repeating of course)% chance to get 0/5 the first time.

It's then a matter of figuring out how many totally different pairs of arrangements can be pulled from that 44 where the placements themselves don't at all match each other (counting each pair twice because they could be played in either order), and dividing that number by 120*120.

Not sure of a good way to do that without exhaustively going through the 44 arrangements and comparing each pair, but for certain, the chance is no larger than (44*43)/(120*120) ~= 13%.
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clemon79

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TPIR math problem
« Reply #3 on: August 13, 2008, 10:57:33 PM »
[quote name=\'Speedy G\' post=\'193969\' date=\'Aug 13 2008, 07:28 PM\']
That's 36.6 (repeating of course)%[/quote]
Approves
« Last Edit: August 13, 2008, 10:58:24 PM by clemon79 »
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Sonic Whammy

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TPIR math problem
« Reply #4 on: August 16, 2008, 11:04:47 PM »
Being the math teacher here, especially a probability lover, I couldn't resist this one.

First, everything about the first attempt is correct. I have it all mapped out here. Unfortunately, at the moment, I can't give you a definite method of working out the second attempt, either. I'll accept the challenge, but for now, at least, I HAVE spelled out all the remaining possibilities, and the final accurate percentage turns out to be:

44/120 x 12/120 = 528/14400 = 3.66...%

So that's the true percentage. I'll get back to you when I know how to calculate the 10% on the second attempt.
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Brian Sapinski

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Matt Ottinger

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TPIR math problem
« Reply #5 on: August 17, 2008, 12:14:03 AM »
[quote name=\'Sonic Whammy\' post=\'194326\' date=\'Aug 16 2008, 11:04 PM\']
Being the math teacher here, especially a probability lover, I couldn't resist this one.[/quote]
Since math teachers may not be as familiar with the improper use of definite articles....

You are certainly not "the" math teacher here.  You are "a" math teacher here.  Offhand I know of two others, and there may be many more.
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Kevin Prather

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TPIR math problem
« Reply #6 on: August 17, 2008, 12:59:24 AM »
[quote name=\'Matt Ottinger\' post=\'194330\' date=\'Aug 16 2008, 09:14 PM\']
[quote name=\'Sonic Whammy\' post=\'194326\' date=\'Aug 16 2008, 11:04 PM\']
Being the math teacher here, especially a probability lover, I couldn't resist this one.[/quote]
Since math teachers may not be as familiar with the improper use of definite articles....

You are certainly not "the" math teacher here.  You are "a" math teacher here.  Offhand I know of two others, and there may be many more.
[/quote]
Maybe by "here", he meant "in his bedroom." :)

/Unless his wife is a math teacher.
//Add a bed, subtract the clothes, divide the legs and multiply.
« Last Edit: August 17, 2008, 12:59:56 AM by Kevin Prather »
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Jay Temple

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TPIR math problem
« Reply #7 on: August 17, 2008, 01:16:24 PM »
[quote name=\'Kevin Prather\' post=\'194333\' date=\'Aug 16 2008, 11:59 PM\']//Add a bed, subtract the clothes, divide the legs and multiply.
[/quote]
That must be the Catholic/Fundamentalist version. I heard it as, "... and pray you don't multiply."
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Sonic Whammy

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TPIR math problem
« Reply #8 on: August 18, 2008, 02:48:25 AM »
[quote name=\'Kevin Prather\' post=\'194333\' date=\'Aug 17 2008, 12:59 AM\']
[quote name=\'Matt Ottinger\' post=\'194330\' date=\'Aug 16 2008, 09:14 PM\']
Since math teachers may not be as familiar with the improper use of definite articles....

You are certainly not "the" math teacher here.  You are "a" math teacher here.  Offhand I know of two others, and there may be many more.
[/quote]
Maybe by "here", he meant "in his bedroom." :)

/Unless his wife is a math teacher.
//Add a bed, subtract the clothes, divide the legs and multiply.
[/quote]
LOL! You guys are mean, sick and crazy all at the same time. And I mean that in a good way.

What makes it funnier, Kevin, is the fact that Andrea and I ARE multiplying. Our first is due New Year's, and we're gonna find out the gender on Friday. We can't wait.

And Matt, you're absolutely right, I know Hammett is, too. That just happened to be what I wrote at the time. But I don't know how he or any of the others feel towards probability, so...

Ah well.
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Brian Sapinski

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MikeK

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TPIR math problem
« Reply #9 on: August 18, 2008, 04:48:05 PM »
[quote name=\'Sonic Whammy\' post=\'194388\' date=\'Aug 18 2008, 02:48 AM\']And Matt, you're absolutely right, I know Hammett is, too. That just happened to be what I wrote at the time. But I don't know how he or any of the others feel towards probability, so...[/quote]
Hrmph.  And probability is one of my favorite subjects with my students.  They love playing and analyzing the different versions of Deal or No Deal.
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Fedya

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TPIR math problem
« Reply #10 on: August 18, 2008, 04:56:14 PM »
Sonic Whammy wrote:
Quote
What makes it funnier, Kevin, is the fact that Andrea and I ARE multiplying. Our first is due New Year's, and we're gonna find out the gender on Friday. We can't wait.
Congratulations.  Nine minutes of passion for you; nine months of work for her.  :-p
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clemon79

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TPIR math problem
« Reply #11 on: August 18, 2008, 06:52:26 PM »
[quote name=\'Fedya\' post=\'194413\' date=\'Aug 18 2008, 01:56 PM\']
Congratulations.  Nine minutes of passion for you; nine months of work for her.  :-p[/quote]
My buddy's kid is two and a half. Rest assured that Sapinski will be doing his fair share of work in the coming years... :)

/nine minutes?
//impressive
///what?
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