jzbao
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• @2018-06-27

## 用chatGPT解数学竞赛题，很逗

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?

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)

where:

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)]

≈ 0.636

Therefore, the probability that the ball came from box A given that it was green is approximately 0.636 or 63.6%.

shanggj
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jzbao
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nickbear
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• @2022-03-17

jzbao 发表于 2023-03-17 18:09

chatGPT回答质量取决于类似的题目在网上有没有答案

shanggj
• 大校
• 6520
• 8
• 6522
• 0
• @2020-09-14

chatGPT回答质量取决于类似的题目在网上有没有答案

nickbear 发表于 2023-03-17 18:12

chatGPT plus user 不是说都可以　access 4.0 吗？

Parlindome
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• @2015-01-04

page394
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jzbao 发表于 2023-03-17 18:09

BeHappy78
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• @2012-03-31

chatGPT回答质量取决于类似的题目在网上有没有答案

nickbear 发表于 2023-03-17 18:12

netghost
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