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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.

07-03-2003, 01:16 PM
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..