I need a math/stats geek momentarily - GoFuckYourself.com

FATPad · 07-03-2003, 11:51 AM

There are four 7 game baseball series going on at once. Once a team wins 4 games the series is over. So a series can go either 4, 5, 6, or 7 games.

What are the chances that 3 of the series go 7 games, but not all 4 do it?

Ignore player abilities and all that. I just want a straight math percentage.

PowerCum · 07-03-2003, 11:57 AM

exactly 50%

They can do it or they cannot.

DTK · 07-03-2003, 12:00 PM

1 in 64 i think

fiveyes · 07-03-2003, 01:16 PM

Half of all the possibilities can be shown as (swap X for O for the other half):

XXXX - 2

XXXOX - 8
XXOXX
XOXXX
OXXXX

XXXOOX - 20
XXOXOX
XOXXOX
OXXXOX
XXOOXX
XOXOXX
OXXOXX
XOOXXX
OXOXXX
OOXXXX

XXXOOOX - 22
XXOXOOX
XOXXOOX
OXXXOOX
XXOOOXX
XOXOOXX
OXXOOXX
XOOOXXX
OOXOXXX
OXOOXXX
OOOXXXX

So, we have 52 possible outcomes. There's a 22/52 chance that any one series will go 7 games and 30/52 chance it won't. We have four series and for three, and only three, of those series to be 7 games long ->

number of ways A does happen
_____________________________ ..... OR .... P(A)/ (1 -P(A))
number of ways A does not happen

Where:
P(A) = 22/52 * 22/52 * 22/52 * 30/52 * 4 = 1277760/7311616

1 - P(A) = (22/52 * 22/52 * 22/52 *22/52) + (30/52 * 30/52 * 22/52 * 22/52 * 6) + (30/52 *30/52 * 30/52 * 22/52 * 4) + (30/52 * 30/52 * 30/52 * 30/52) =
(234256 + 2613600 + 2376000 + 810000)/7311616 = 7077360/7311616

(1277760/7311616)
__________________ = 1277760/7077360 =
(7077360/7311616)

5324/29489 or about an 18% chance.

Penthouse_mike · 07-03-2003, 02:00 PM

22/52*22/52*22/52*30/52

4.36%

Edited: to remove geeky exposition

fiveyes · 07-03-2003, 02:45 PM

Quote:

Originally posted by Penthouse_mike
22/52*22/52*22/52*30/52

4.36%

Edited: to remove geeky exposition

What you're showing is the possibilty of any one specific match of a series being the only one not 7 games long.

Look at it this way- There are four series to be played, and three of them must be 7 games and one of the others is of 4-6 games.

OK, label each of the series A-D, but use lower case to designate the 4-6 game set. You'll then see there are 4 possible permutations:
a-B-C-D = 30/52*22/52*22/52*22/52
A-b-C-D = 22/52*30/52*22/52*22/52
A-B-c-D = 22/52*22/52*30/52*22/52
A-B-C-d = 22/52*22/52*22/52*30/52

This is how P(A), the number of possible ways, is derived. So we have 22/52*22/52*22/52*30/52*4. But that has to be divided by 1 - P(A), the number of ways it doesn't happen, to give the odds.

fiveyes · 07-03-2003, 04:43 PM

Got an e-mail that shows a bit of lack of understanding on what "odds" are, so one last time in...

See http://www.saintjoe.edu/~karend/m111/m111c7.html for the difference between "probability" (P(A)), and "odds" (P(A)/P(not A)). Also check on the definition of "sample space".

Breakdown of the complete sample space, using UPPER CASE to show a seven game match:

a-B-C-D = 30/52*22/52*22/52*22/52 | These
A-b-C-D = 22/52*30/52*22/52*22/52 | meet
A-B-c-D = 22/52*22/52*30/52*22/52 | the
A-B-C-d = 22/52*22/52*22/52*30/52 | criteria.
__________________________________________
a-b-c-d | No 7 game matches. (30/52*30/52*30/52*30/52) +

A-b-c-d | Just
a-B-c-d | one match
a-b-C-d | of 7
a-b-c-D | games. (30/52*30/52*30/52*22/52*4) +

a-b-C-D | Two
a-B-c-D | matches
A-b-c-D | of
a-B-C-d | 7
A-b-C-d | games
A-B-c-d | each. (30/52*30/52*22/52*22/52*6) +

A-B-C-D | All 7 game matches. (22/52*22/52*22/52*22/52)

~~~~~~~

So, the odds are app. 3/20, 3:20, 3 to 20 or, as a percentage, 15%.

Amputate Your Head · 07-03-2003, 04:44 PM

Brazzer · 07-03-2003, 06:16 PM

answer is :

12/256

Peace

FATPad · 07-04-2003, 06:58 AM

Thanks, folks.

07-03-2003, 11:51 AM	#1
FATPad Confirmed User Join Date: Oct 2001 Posts: 6,693	I need a math/stats geek momentarily There are four 7 game baseball series going on at once. Once a team wins 4 games the series is over. So a series can go either 4, 5, 6, or 7 games. What are the chances that 3 of the series go 7 games, but not all 4 do it? Ignore player abilities and all that. I just want a straight math percentage. __________________ <a href="http://www.adultcontent.co.uk">Adult Content UK - Great British Content</a>

07-03-2003, 11:57 AM	#2
PowerCum CjOverkill Industry Role: Join Date: Apr 2003 Location: Woldwide Posts: 1,328	exactly 50% They can do it or they cannot. __________________ CjOverkill Traffic Trading Script Free, secure and fast traffic trading script. Get your copy now

07-03-2003, 01:16 PM	#4
fiveyes Confirmed User Join Date: Aug 2001 Location: New Orleans Posts: 1,680	Half of all the possibilities can be shown as (swap X for O for the other half): XXXX - 2 XXXOX - 8 XXOXX XOXXX OXXXX XXXOOX - 20 XXOXOX XOXXOX OXXXOX XXOOXX XOXOXX OXXOXX XOOXXX OXOXXX OOXXXX XXXOOOX - 22 XXOXOOX XOXXOOX OXXXOOX XXOOOXX XOXOOXX OXXOOXX XOOOXXX OOXOXXX OXOOXXX OOOXXXX So, we have 52 possible outcomes. There's a 22/52 chance that any one series will go 7 games and 30/52 chance it won't. We have four series and for three, and only three, of those series to be 7 games long -> number of ways A does happen _____________________________ ..... OR .... P(A)/ (1 -P(A)) number of ways A does not happen Where: P(A) = 22/52 * 22/52 * 22/52 * 30/52 * 4 = 1277760/7311616 1 - P(A) = (22/52 * 22/52 * 22/52 22/52) + (30/52 30/52 * 22/52 * 22/52 * 6) + (30/52 30/52 30/52 * 22/52 * 4) + (30/52 * 30/52 * 30/52 * 30/52) = (234256 + 2613600 + 2376000 + 810000)/7311616 = 7077360/7311616 (1277760/7311616) __________________ = 1277760/7077360 = (7077360/7311616) 5324/29489 or about an 18% chance. __________________ <CENTER><A HREF="http://www.hot-off-bourbon.com/" target="_blank"><IMG SRC="http://www.hot-off-bourbon.com/images/hob-logosmall.jpg" border="0"></A> <FONT face="Comic Sans MS" SIZE="-1"><I>Mardi Gras, Spring Break, Wet-T, Night Club Action, UpSkirt, Oil Wrestling, Voyeur</I></FONT></CENTER> Last edited by fiveyes; 07-03-2003 at 01:18 PM..

07-03-2003, 02:00 PM	#5
Penthouse_mike Confirmed User Industry Role: Join Date: Jun 2003 Location: Silicon Valley Posts: 317	22/5222/5222/5230/52 4.36% Edited: to remove geeky exposition Last edited by Penthouse_mike; 07-03-2003 at 02:05 PM..*

07-03-2003, 04:43 PM	#7
fiveyes Confirmed User Join Date: Aug 2001 Location: New Orleans Posts: 1,680	Got an e-mail that shows a bit of lack of understanding on what "odds" are, so one last time in... See http://www.saintjoe.edu/~karend/m111/m111c7.html for the difference between "probability" (P(A)), and "odds" (P(A)/P(not A)). Also check on the definition of "sample space". Breakdown of the <B>complete</B> sample space, using UPPER CASE to show a seven game match: a-B-C-D = 30/5222/5222/5222/52 \| These A-b-C-D = 22/5230/5222/5222/52 \| meet A-B-c-D = 22/5222/5230/5222/52 \| the A-B-C-d = 22/5222/5222/5230/52 \| criteria. __________________________________________ a-b-c-d \| No 7 game matches. (30/5230/5230/5230/52) + A-b-c-d \| Just a-B-c-d \| one match a-b-C-d \| of 7 a-b-c-D \| games. (30/5230/5230/5222/524) + a-b-C-D \| Two a-B-c-D \| matches A-b-c-D \| of a-B-C-d \| 7 A-b-C-d \| games A-B-c-d \| each. (30/5230/5222/5222/526) + A-B-C-D \| All 7 game matches. (22/5222/5222/5222/52) ~~~~~~~ So, the odds are app. 3/20, 3:20, 3 to 20 or, as a percentage, 15%. __________________ <CENTER><A HREF="http://www.hot-off-bourbon.com/" target="_blank"><IMG SRC="http://www.hot-off-bourbon.com/images/hob-logosmall.jpg" border="0"></A> <FONT face="Comic Sans MS" SIZE="-1"><I>Mardi Gras, Spring Break, Wet-T, Night Club Action, UpSkirt, Oil Wrestling, Voyeur</I></FONT></CENTER> Last edited by fiveyes; 07-03-2003 at 04:45 PM..

07-03-2003, 12:00 PM	#3
DTK Confirmed User Industry Role: Join Date: Feb 2002 Location: The 510 Posts: 4,545	1 in 64 i think

07-03-2003, 04:44 PM	#8
Amputate Your Head There can be only one Industry Role: Join Date: Aug 2001 Location: Somewhere else Posts: 39,075	__________________ SIG TOO BIG

07-03-2003, 06:16 PM	#9
Brazzer Confirmed User Join Date: Mar 2003 Posts: 400	answer is : 12/256 Peace

07-04-2003, 06:58 AM	#10
FATPad Confirmed User Join Date: Oct 2001 Posts: 6,693	Thanks, folks. __________________ <a href="http://www.adultcontent.co.uk">Adult Content UK - Great British Content</a>