Answer: P(A) = sum of P(A|Bi)×P(Bi) for a partition {B1,...,Bn} of sample space.
- A P(A) = sum of P(A|Bi)×P(Bi) for a partition {B1,...,Bn} of sample space
- B P(A) = P(A|B), treating conditioning as having no effect
- C P(A) = 1 - P(A), solved incorrectly as if A were its own complement
- D P(A ∩ B) = P(A)P(B), valid only under an unstated independence assumption
Correct answer: A. P(A) = sum of P(A|Bi)×P(Bi) for a partition {B1,...,Bn} of sample space
Explanation: Law of total probability: if B1,...,Bn is a partition of S, then P(A) = sum P(A|Bi)P(Bi). Used in Bayes' theorem.
Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.
Concept context
Chance, events, conditional probability, and Bayes theorem