Question

What must be true in order for P (A or B)= P(a) • P(b)

Answer 1

`\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)`

If
`A` and
`B` are independent, then
`\mathbb P(A\cap B)=\mathbb P(A)\mathbb P(B)`, so under this assumption


`\mathbb P(A)\mathbb P(B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cup B)`

The only way for
`\mathbb P(A\cup B)` to be equal to
`\mathbb P(A)\mathbb P(B)` is if both
`\mathbb P(A)` and
`\mathbb P(B)` are zero.