Let and be Sets. Conditional Probability requires that
|
(1) |
where denotes Intersection (``and''), and also that
|
(2) |
and
|
(3) |
Since (2) and (3) must be equal,
|
(4) |
From (2) and (3),
|
(5) |
Equating (5) with (2) gives
|
(6) |
so
|
(7) |
Now, let
|
(8) |
so is an event in and
for , then
|
(9) |
|
(10) |
From (5), this becomes
|
(11) |
so
|
(12) |
See also Conditional Probability, Independent Statistics
References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge
University Press, p. 810, 1992.
© 1996-9 Eric W. Weisstein
1999-05-26