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The addition theorem of probability can ...

The addition theorem of probability can be written easily using the following ways :
`P(A cup B)=S_1 - S_2`
`P(A cup B cup C)= S_1-S_2 + S_3 `
Where `S_1 to ` Sum of probability of events taken one at a time .
`S_2 to ` Sum of probability of events taken two at time .
`S_3 to ` Sum of prbability of evants taken three at time.
`P ( A cup B)= underset(S_1)(ubrace(P(A) + P(B)))" " underset(S_2)(ubrace(P(A cap B)))`
`P( A cup B cup C)= underset(S_1)(ubrace(P(A)+P(B)+P(C)))`
` underset(S_2)(ubrace((P( A cap B) + P( B cap C) +P ( A cap C ))))underset (S_3)( ubrace(P(A cap B cap C)))`
Find the probability of `P ( A cup B cup C cup D)` using the above way . Can you find a pattern for the number of terms in the formula ?

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