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The multiplication rule for probability states P(E ∩ F) equals
A{'text': 'P(E) × P(F) always', 'label': 'A'}
B{'text': 'P(E) + P(F)', 'label': 'B'}
C{'text': 'P(F|E) × P(E), if P(E) > 0', 'label': 'C'}
D{'text': 'P(E) / P(F)', 'label': 'D'}
Answer & Solution
Correct answer: C. {'text': 'P(F|E) × P(E), if P(E) > 0', 'label': 'C'}
1. Multiplication rule follows directly from the definition P(F|E) = P(E ∩ F) / P(E).
2. Rearranging: P(E ∩ F) = P(E) × P(F|E), valid for P(E) > 0.
3. Equivalently P(E ∩ F) = P(F) × P(E|F).
4. Independence gives the simplified form P(E ∩ F) = P(E) × P(F).
_Source: NCERT Class 12 Mathematics, Ch 13 "Probability", §13.3_
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