Two events E and F are called independent if

Question

Accepted 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_

Answer

{'text': 'P(E ∪ F) = P(E) + P(F)', 'label': 'A'}

Answer

{'text': 'E ∩ F = φ', 'label': 'B'}

Answer

{'text': 'P(E|F) = P(F|E)', 'label': 'C'}