Question

Are disjoint events independent?

Answer 1

For disjoint `P(A \cap B) = 0`

For independence, `P(A \cap B) = P(A) * P(B)`

If two disjoint events are independent then `P(A \cap B) = 0 = P(A) * P(B)`

`=> P(A) = 0` or `P(B) = 0`

So, either of those events is impossible. Two positive disjoint events cannot be independent.