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Bertrand's Box Surprise

Medium · Probability & Statistics · Quant Trader interview question · probability, conditional-probability, bayes-theorem

You are presented with three boxes. Box 1 contains two gold coins. Box 2 contains two silver coins. Box 3 contains one gold coin and one silver coin. You randomly select a box and then randomly draw a coin from that box. Given that the coin you drew is gold, what is the probability that the other coin in the box you selected is also gold?