Mutually exclusive and independent events – UGC NET Question

Statements A, B, C and D together summarise the standard relationships between mutually exclusive and independent events. A correctly defines mutual exclusivity as events that cannot happen simultaneously. B properly describes independence in terms of unchanged probabilities. C follows because if two non-trivial events are mutually exclusive, their joint probability is zero and cannot equal the product of positive probabilities, so they are not independent. D restates the formal definition of independence using the product rule. E is false since mutual exclusivity and independence are distinct concepts, so the correct set is A, B, C and D only.

Option A:
Option A is incomplete because it omits D and thus fails to express the formal product definition of independence, even though A, B and C are true. The absence of D makes the description of independence less precise.

Option B:
Option B is correct as it combines the basic definitions and implications about mutual exclusivity and independence and excludes E, which wrongly equates the two. It matches the conceptual treatment of events found in NET-level probability questions.

Option C:
Option C is incorrect because it includes E, the false claim that mutual exclusivity and independence mean the same thing, and leaves out B, which is a core statement about independence. This mixture of error and omission invalidates the option.

Option D:
Option D is wrong as it drops A and includes only B, C and D, leaving out the explicit definition of mutual exclusivity while still not rejecting E. It therefore does not provide the complete and correct set of statements.