Suppose event A and event B are independent. Which of the following is an example of the conjunction bias?
A) $P(A \cap B) \leq P(A)$
B) $P(A \cap B) \leq P(B)$
C) $P(A \cup B) \geq P(B)$
D) $P(A \cap B)P(B)$

Question

Suppose event A and event B are independent. Which of the following is an example of the conjunction bias?
A) $P(A \cap B) \leq P(A)$
B) $P(A \cap B) \leq P(B)$
C) $P(A \cup B) \geq P(B)$
D) $P(A \cap B)>P(B)$

Quizplus · Accepted Answer

The conjunction bias is the fallacy where people assume that specific conditions are more probable than a single general one. For independent events A and B, the probability of both A and B occurring together ($P(A \cap B)$) should be less than or equal to the probability of either event occurring alone ($P(A)$ or $P(B)$). Option D suggests that the probability of A and B occurring together is greater than the probability of B occurring alone, which is a misconception and an example of the conjunction bias.

Suppose Event a and Event B Are Independent P(A∩B)≤P(A)P(A \cap B) \leq P(A)P(A∩B)≤P(A)

Suppose Event a and Event B Are Independent $P(A \cap B) \leq P(A)$