In cognitive psychology, what does the conjunction rule state?

• A. The probability of two events occurring together cannot be greater than the probability of either event occurring alone.
• B. The probability of two events occurring together is unrelated to the probability of either event occurring alone.
• C. The probability of two events occurring together is always equal to the probability of one event occurring alone.
• D. The probability of two events occurring together is always less than the probability of either event occurring alone.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand that the conjunction rule is a principle from probability theory applied in cognitive psychology to explain how people judge the likelihood of combined events.
2. Step 2: Recognize that the conjunction rule states a relationship between the probability of two events occurring together (conjunction) and the probabilities of each event occurring individually.
3. Step 3: Recall the formal expression of the conjunction rule: the probability of the conjunction of two events A and B, denoted as \(P(A \cap B)\), cannot be greater than the probability of either event alone, i.e., \(P(A \cap B) \leq P(A)\) and \(P(A \cap B) \leq P(B)\).
4. Step 4: Understand that this means when people estimate the likelihood of two events happening together, it should logically be less than or equal to the likelihood of each event happening separately.
5. Step 5: Note that violations of this rule in human judgment are known as the conjunction fallacy, where people incorrectly judge the conjunction as more probable than one of the single events.