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. 1/3

  2. 2/3

  3. 1/2

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Classic conditional probability (Bayesian reasoning). You drew a white marble. This could come from Bag A (2 white) or Bag C (1 white, 1 black), not Bag B (2 black). Given white marble, probability you picked Bag A is 2/3 (2 white marbles in A vs 1 in C). If from Bag A, remaining marble is white. So answer = 2/3. This is not 1/3 (that's the prior probability of picking Bag A), not 1/2 (ignoring the evidence).

AI explanation

Out of the 6 marbles, 3 are white: 2 from bag A and 1 from bag C. Given that a white marble was drawn, each of those 3 white marbles is equally likely to be the one picked. In 2 of those 3 equally likely cases the marble came from bag A, whose remaining marble is also white, giving a probability of 2/3.

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