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Q.
If two events are independent, then
Probability - Part 2
Solution:
If two events $A$ and $B$ are independent, then we know that $P ( A \cap B )= P ( A ) \cdot P ( B ), P ( A ) \neq 0 , P ( B ) \neq 0$
Since, $A$ and $B$ have a common outcome. Further, mutually exclusive events never have a common outcome.
In other words, two independents events having non-zero probabilities of occurrence cannot be mutually exclusive and conversely, i.e., two mutually exclusive events having nonzero probabilities of outcome cannot be independent.