Flashcards · 7357 · Topic 14

M: Probability flashcards

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Complement rule and addition rule: P(A′) = 1 − P(A). P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Mutually exclusive events: They cannot happen together: P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
Independent events: One does not affect the other: P(A ∩ B) = P(A) × P(B), equivalently P(A | B) = P(A).
Conditional probability and the multiplication rule: P(A | B) = P(A ∩ B)/P(B), for P(B) > 0. P(A ∩ B) = P(B) × P(A | B), used along tree branches.
P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2. Are A and B independent? Find P(A ∪ B).: P(A) × P(B) = 0.2 = P(A ∩ B), so they are independent. P(A ∪ B) = 0.5 + 0.4 − 0.2 = 0.7.
The easiest way to find P(at least one): 1 − P(none).
Can two events with non-zero probabilities be both mutually exclusive and independent?: No: mutually exclusive means P(A ∩ B) = 0, but independence needs P(A ∩ B) = P(A)P(B) > 0.