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?
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.
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