Question

P(A) = 1/4, P(B) = 2/3, P(A and B) = 1/6. Are Events A and B independent?

Answer 1

For
`A` and
`B` to be independent, it must be the case that


`\mathbb P(A\cap B)=\mathbb P(A)*\mathbb P(B)`

You're given


`\mathbb P(A\cap B)=\frac16`

while


`\mathbb P(A)*\mathbb P(B)=\frac14*\frac23=\frac16`

So yes, the two events are independent.