Which statement best describes the conjunction rule of probability?

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BlackTom AI · Accepted Answer

Question restatement: The prompt asks for the option that best describes the conjunction rule of probability.
Option 1: 'Two events are never more likely to occur together than either of the two events' This aligns with the fundamental idea that the probability of A and B occurring cannot exceed the probability of A alone or B alone. In formal terms, P(A ∩ B) ≤ P(A) and P(A ∩ B) ≤ P(B); the joint occurrence is constrained by each individual event's likelihood. The minimum of P(A) and P(B) is an upper bound for P(A ∩ B), so this statement is consistent with the conjunction rule.
Option 2: 'Participants often assign higher likelihoods to two events occurring together than either of the individual events' This describes a common cognitive bias or misperception, not a mathematical truth about conjunctions. In probability theory, there is no general rule that makes joint events more probable than the individual events; in fact, the joint probability is typically less than or equal to each individual probability. Therefore this statement is incorrect.
Option 3: 'One event is always more likely to occur than another' This is a comparison between two single events and says nothing about their conjunction. It asserts a relative likelihood that does not capture the essence of P(A ∩ B) versus P(A) or P(B). As a description of the conjunction rule, it’s inaccurate.
Option 4: 'Two events are more likely to occur together than either of the individual events' This claim contradicts the basic principle of joint probability: the probability of both events happening is constrained by the individual probabilities and cannot exceed them. In most cases P(A ∩ B) ≤ P(A) and P(A ∩ B) ≤ P(B); asserting it is greater than both individual probabilities is generally false.

PSYC20007_2025_SM2 Supplementary or Special Exam: Cognitive Psychology (PSYC20007_2025_SM2)- Requires Respondus LockDown Browser

Which statement best describes the conjunction rule of probability?

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