Three boxes of medals

Question

Three closed boxes each hold two medals. One box has two gold medals, one box has two bronze medals, and one box has one gold and one bronze. You pick a box at random, reach in, and pull out one medal at random. It is gold.

What is the probability that the other medal in that same box is also gold?

Accepted Answer

The instinct is to say 	frac{1}{2}: "it is either the gold-gold box or the mixed box, so even odds." That reasoning forgets that a gold-gold box gives you two chances to draw gold, while the mixed box gives only one. Count the individual gold medals, since each equally likely medal you might have drawn is what matters. There are three gold medals in play: - 2 gold medals in the gold-gold box, and - 1 gold medal in the mixed box. You are equally likely to be holding any of these three golds. For two of them (the pair in the gold-gold box), the partner medal is gold. For one of them (the mixed…

Three boxes of medals

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