Question

If A and B are any two events of S and \[P(F)\neq 0\], which formula is correct?

Options

• \[P((A\cup B)\mid F)=1-P((A\cap B)\mid F)\]

• \[P((A\cup B)\mid F)=P(A\mid F)+P(B\mid F)-P((A\cap B)\mid F)\]

• \[P((A\cup B)\mid F)=P(A\mid F)+P(B\mid F)+P((A\cap B)\mid F)\]

• \[P((A\cup B)\mid F)=P(A\mid F)\cdot P(B\mid F)\]

Answer 1

The probabilities of A and B under F are added, but common outcomes are counted twice. Therefore \[P((A\cap B)\mid F)\] must be subtracted once.