You reach the end of the rainbow and a leprechaun offers you your choice of thre

Question

You reach the end of the rainbow and a leprechaun offers you your choice of three identical looking pots. The leprechaun tells you that one of the pots contains two gold coins, one contains two silver coins, and one contains a gold and a silver coin. You are not allowed to inspect the pots or their contents before making your choice, so you choose one of the pots at random. After being given the pot, you reach in and randomly take out one of the two coins in it, without looking at the other. If the coin you took out happens to be gold, what is the probability that the other coin in the pot is also gold?

Explanation / Answer

For ease of out calculation, Let us denote the 3 pots as:

A: 2 silver coins

B: 1 gold and 1 silver coin

C: 2 gold coins

The probability of each one being selected is equally probable and each is equal to 1/3.

Probability of the other coin being gold, given that the first coin is gold = probability of selecting pot C / probability of selecting either pot B or pot C = (1/3) / (1/3 + 1/3) = 1/2

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