is the sample space. Then .
And .
Hence .
Bonferroni's Inequality states that:
But the first axiom of probability states that:
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Am I allowed to do the following?
And the last line must be true because the entire sample size must be at least equal to the union of A and B minus their intersection.
OR
Should i rather try to prove it this way:
Rearrange so that the 1 is isolated...
Which is also true...
Anyone got an idea which one of these is correct?
Thanks in advance.
EDIT: The second one might be the correct one seeing as A and B are not disjoint. Am i right?