alleryTwo events $A$ and $B$ are MUTUALLY EXCLUSIVE if
A$P(A) = P(B)$
B$P(A) + P(B) = 1$
C$A \cap B = \emptyset$
D$A = B$
Answer & Solution
Correct answer: C. $A \cap B = \emptyset$
1. Your syllabus: two events are MUTUALLY EXCLUSIVE (or DISJOINT) when they cannot occur SIMULTANEOUSLY.
2. Formally: $A \cap B = \emptyset$ — no outcome lies in both events.
3. Consequence: $P(A \cap B) = 0$ for mutually exclusive events, and the addition rule simplifies to $P(A \cup B) = P(A) + P(B)$.
4. Examples: rolling a die — 'showing 1' and 'showing 6' are mutually exclusive; 'odd' and 'even' are mutually exclusive AND exhaustive.
5. Options A, B, D describe different relationships (equal probabilities, exhaustive together, identical events) — not mutual exclusion.
_Source: syllabus Mathematics, Ch 14, §14.1 (Mutually exclusive events), p. 2._
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