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Diffstat (limited to 'houdre/hw1.tex')
-rw-r--r-- | houdre/hw1.tex | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/houdre/hw1.tex b/houdre/hw1.tex index c06f5fa..e49bd49 100644 --- a/houdre/hw1.tex +++ b/houdre/hw1.tex @@ -144,7 +144,7 @@ $$\Pr(A\cup B) = \Pr(A\setminus B)+\Pr(B\setminus A)+\Pr(A\cap B)$$ $$= (\Pr(A\setminus B)+\Pr(A\cap B)) + (\Pr(B\setminus A)+\Pr(A\cap B)) - \Pr(A\cap B)$$ $$= \Pr(A) + \Pr(B) - \Pr(A\cap B) -= \sum_i \Pr(A_i) - \sum_{i<j} \Pr(A_i\cap A_j).$$ += \sum_i \Pr(A_i) - \sum_{i<j} \Pr(A_i\cap A_j).$$ Let the above be considered a base case, with the successive case $U_n = U_{n-1}\cup A_n.$ |