Multiple choice general knowledge math & puzzles

You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. You pick a random bag and take out one marble. It is a white marble. What is the probability that the remaining marble from the same bag is also white?

  1. 2/3

  2. 1/2

  3. 2/4

  4. 4/7
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A Correct answer
Explanation

Using Bayes' theorem or simple counting: there are 3 white marbles total, and 2 of them are in Bag A (where the remaining is white). If you drew a white marble, the probability it came from Bag A is 2/3. Only Bag A guarantees a white remaining; Bag C has a black remaining. Therefore the probability is 2/3.

AI explanation

This is a Bertrand's box paradox variant. Treat all 6 marbles as equally likely to be the one drawn. There are 3 white marbles total: 2 in Bag A, 1 in Bag C. Given that a white marble was drawn, the probability it came from Bag A is 2/3 (since 2 of the 3 white marbles are in Bag A), and 1/3 that it came from Bag C. If it came from Bag A, the remaining marble is definitely white; if from Bag C, the remaining marble is black. So P(remaining is white) = 2/3. The naive answer of 1/2 (ignoring that Bag A offers two ways to draw white but Bag C only one) is the classic wrong intuition this puzzle is designed to expose.

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