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Two events E and F are called independent if
A{'text': 'P(E ∪ F) = P(E) + P(F)', 'label': 'A'}
B{'text': 'E ∩ F = φ', 'label': 'B'}
C{'text': 'P(E|F) = P(F|E)', 'label': 'C'}
D{'text': 'P(E ∩ F) = P(E) × P(F)', 'label': 'D'}
Answer & Solution
Correct answer: D. {'text': 'P(E ∩ F) = P(E) × P(F)', 'label': 'D'}
1. Independent events are those where knowing one occurred does not change the probability of the other.
2. Equivalent formal statement: P(E ∩ F) = P(E) × P(F).
3. Two other equivalents: P(E|F) = P(E) and P(F|E) = P(F).
4. Mutually exclusive events (E ∩ F = φ) are generally NOT independent unless one has zero probability.
_Source: NCERT Class 12 Mathematics, Ch 13 "Probability", §13.4_
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