AP Statistics / Mr. Hansen
11/30/1999

Six coins (3 gold, 3 silver) are stored in a chest of 3 drawers in the following way: one drawer has 2 gold coins, one drawer has 2 silver coins, and the remaining drawer has 1 gold and 1 silver coin. The drawers have been randomly scrambled so that you have no idea which drawer has the 2 gold coins, which drawer has the 2 silver coins, and which drawer has 1 gold and 1 silver coin.

You select a drawer at random and withdraw a coin at random, without looking at the other one in the same drawer. If the coin you selected is gold, what is the probability that the other coin in the same drawer is also gold?

Use the same coins (3 gold, 3 silver) as before, but this time, use a thorough randomization procedure to scramble not the drawers, but the coins themselves. In other words, there are still 2 positions available in each drawer, but the 6 coins are randomly scrambled so as to fill those 6 positions. Note that this time there is no guarantee that the drawers will have 2 silver coins, 2 gold coins, and 1 gold/1 silver, since you could end up having 1 gold and 1 silver coin in each of the drawers.

Answer the same question as before: You select a drawer at random and withdraw a coin at random, without looking at the other one in the same drawer. If the coin you selected is gold, what is the probability that the other coin in the same drawer is also gold?