Probability - Breaking up an event into unions of complements

[IniquiTrance]

Why is it that given 3 events, A, B, and C describe a sample space, then:

P(A) = P(AB^CC^C) + P(ABC)

Shouldn't it be:

P(A) = P(ABC) + P(ABC^C) +P(AB^CC) +P(AB^CC^C)

Thanks!

 

[tiny-tim]

Hi IniquiTrance!

Yes.