Question

P(A) = 1/2, P(B) = 1/3, P(A or B) = 2/3. Are A and B mutually exclusive?

Answer 1

`A` and
`B` are mutually exclusive if


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

You have


`\frac12+\frac13=\frac56\\eq\frac23`

so the answer is no.