Question

Suppose there are two disjoint events A and B. Each of them has positive probability. What can you say about independence of A and B?

  1. Both are independent
  2. They are not independent
  3. Canโ€™t say anything

Answer

Two events are said to be independent if \[P(A \cap B) = P(A)P(B)\] In the case of disjoint events: \[P(A \cap B) = P(\phi) = 0\] where \(\phi\) is null set.

Whereas: \[P(A)P(B) > 0\]

So, \(P(A \cap B) \ne P(A)P(B)\). Hence they are not independent.

Thanks for reading. If you like the question, how about some love and coffee: Buy me a coffee