娃正参加Beestar的网上数学竞赛，第二轮有几道题挺难，我看了也不确定，索性下来用正时髦的chatGPT试试，结果让我大开眼界，chatGPT几秒钟解五年级竞赛难题， 并且给出详细推理过程。但chatGPT也在简单的分数计算出错，莫名其妙。。 分享一下：
Box A contains 5 red balls and 7 green balls. Box B contains 3 red balls and 2 green balls. A box is chosen at random, and one ball removed at random from this box. Given that the ball removed was green, what is the probability that it came from box A?
这题目谁碰上都得仔细想想。 输入chatGPT， 几秒钟给出超详细的解题过程：
Let's use Bayes' theorem to solve this problem:
Let A be the event that the ball was drawn from box A, and G be the event that a green ball was drawn. We want to find P(A|G), the probability that the ball came from box A given that it was green.
By Bayes' theorem:
P(A|G) = P(G|A)P(A) / P(G)
P(G|A) is the probability of drawing a green ball given that the box is A. This is 7/12 since box A has 7 green balls out of 12 total balls.
P(A) is the prior probability of choosing box A, which is 1/2 since either box could have been chosen at random.
P(G) is the total probability of drawing a green ball, which can be calculated using the law of total probability:
P(G) = P(G|A)P(A) + P(G|B)P(B)
where P(G|B) is the probability of drawing a green ball given that the box is B, and P(B) is the prior probability of choosing box B, which is also 1/2.
We can calculate P(G|B) as 2/5 since box B has 2 green balls out of 5 total balls.
Plugging these values into Bayes' theorem, we get:
P(A|G) = (7/12) * (1/2) / [(7/12)(1/2) + (2/5)(1/2)]
Therefore, the probability that the ball came from box A given that it was green is approximately 0.636 or 63.6%.
太厉害了！chatGPT 真吓我一跳。但当我拿着结果在Beestar却找不到正确的选则答案。后来知道chatGTP竟把自己给出的简单计算算错了，(7/12) * (1/2) / [(7/12)(1/2) + (2/5)(1/2)] = 35/59 ≈ 0.593， 不是0.636。 难解题思路它都对了，简单计算却错了，让我无语，真逗！搞AI的大牛们解释一下，是不是AI 分数计算能力有点弱？
你用的旧版本吧， 听说新的 ４.０ 没有这种问题了。