April 2016
Intermediate to advanced
478 pages
14h 44m
English
Content preview from Combinatorics of Permutations, 2nd Edition
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Mean and Insensitive. Random Permutations. 245
fore, the total probability that we get a tableaux of shape F is f
F
·
f
F
n!
=
(f
F
)
2
n!
,
proving that
F
(f
F
)
2
n!
=1
as claimed.
We will need the notion of conditional probabilities.
DEFINITION 6.13 Let A and B be two events so that P [B] > 0.Then
we define
P [A|B]=
P [A ∩ B]
P [B]
and we call P [A|B] the probability of A given B.
In other words, P [A|B] is the probability of the occurrence of A if we assume
that B occurs. As we mentioned before, A and B are called independent if
P [A|B]=P [A], that is, if the occurrence of B does not make the occurrence
of A any more or less likely.
One basic and well-known application
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