alleryTwo events E and F are called independent if
AP(E ∪ F) = P(E) + P(F)
BE ∩ F = φ
CP(E|F) = P(F|E)
DP(E ∩ F) = P(E) × P(F)
Answer & Solution
Correct answer: D. P(E ∩ F) = P(E) × P(F)
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: syllabus Mathematics, Ch 13 "Probability", §13.4_
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