位置11的问题 The probability that a student gets a score above 70 on this exam given that they studied is necessarily equal to the probability that a student studied given that they got above a 70 on this exam.TrueFalseDon't Know清除选择

Question

BlackTom AI · Accepted Answer

The question asks whether P(score>70 | studied) is necessarily equal to P(studied | score>70).
Option 1: True. This is not generally correct. In probability, A given B is not the same as B given A unless special symmetry or additional information holds. Here, studying and scoring above 70 are related but not interchangeable events, so the two conditional probabilities are not guaranteed to be equal.
Option 2: False. This is the correct characterization. The equality P(A|B) = P(B|A) would require specific conditions (such as equal priors and a certain form of the joint distribution), which we do not have. In most realistic settings, studying raises the chance of a high score, but the reverse conditional probability is influenced by how common high scores are among all students, so the two quantities differ.
Option 3: Don't Know. While it’s true that conditional probabilities can be subtle, we do have enough foundational reasoning to conclude they are not necessarily equal without extra information. Therefore, choosing this option would indicate uncertainty where a standard probability principle applies.

位置11的问题 The probability that a student gets a score above 70 on this exam given that they studied is necessarily equal to the probability that a student studied given that they got above a 70 on this exam.TrueFalseDon't Know清除选择

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