Math

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Could someone help be understand the general addition rule for probability? It says P(A or B)= P(A)+P(B) - P(A and B). But I get a different answer when I work it out myself:
P(A or B)= P(A)(1-P(B)) +P(B)(1-P(A))
= P(A) -P(A)P(B) +P(B)-P(A)P(B)
=P(A) +P(B) -2P(A)P(B)
Would someone please help me! Thanks :)

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