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3. [Conditional probabilities] There are three boxes, each containing two coins. One box has two gold...

3. [Conditional probabilities] There are three boxes, each containing two coins. One box has two gold coins, another two silver coins, and the third has one gold and one silver coin. One of the three boxes is chosen at random and from that box a coin is drawn at random. Suppose that coin happens to be gold. What is the probability that the remaining coin in the box is also gold? Show your work.

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