Question: S Inclusionexclusion principle. Let . ;F; P/ be a probability space and Ai 2 F, i 2 I D 1; : : : ; n.

S Inclusion–exclusion principle. Let . ;F; P/ be a probability space and Ai 2 F, i 2 I D ¹1; : : : ; nº. For J  I let BJ D

\

j2J Aj \

\

j2InJ Ac j

I by convention, an intersection over an empty index set is equal to . Show the following:

(a) For all K  I , P

 T k2K Ak



D X

KJI P.BJ /:

(b) For all J  I , P.BJ / D X

JKI

.1/

jKnJj P

 T k2K Ak



:

What does this imply for J D ¿?

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