For any two events $A$ and $B$, the probability of $A \cup B$ (A or B) is given by
A$P(A) + P(B)$
B$P(A) + P(B) - P(A \cap B)$
C$P(A) \cdot P(B)$
D$1 - P(A) \cdot P(B)$
Answer & Solution
Correct answer: B. $P(A) + P(B) - P(A \cap B)$
1. NCERT §14.2.3 (Probability of $A \cup B$): the addition rule for probabilities of any two events.
2. Formula: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
3. The subtraction prevents double-counting: outcomes in BOTH A and B are counted once in $P(A)$ AND once in $P(B)$, hence subtracted once via $P(A \cap B)$.
4. Special case: if $A$ and $B$ are MUTUALLY EXCLUSIVE (disjoint), $P(A \cap B) = 0$, so the formula simplifies to $P(A) + P(B)$ — option A's case.
5. Option C is the multiplication rule for INDEPENDENT events (gives $P(A \cap B)$, not $P(A \cup B)$). Option D has no probabilistic interpretation.
_Source: NCERT Class 11 Mathematics, Ch 14, §14.2.3 (Probability of A or B), p. 9–11._
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