Question

If two events are independent, then

• A. they must be mutually exclusive
• B. the sum of their probabilities must be equal to $1$
• C. both (a) and (b) are correct
• D. None of these

Answer 1

Answer: (D)

If two events $A$ and $B$ are independent, then we know that $P(A\cap B)=P(A)\cdot P(B),P(A)\ne 0,P(B)\ne 0$
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.