You have three cabinets. Each of these three cabinets has two drawers. In one of the cabinets, there is a Gold coin in one drawer and a silver in the other. In another there is a gold coin in both drawers. In the last cabinet there is a silver coin in each drawer. Now you walk into the room, not knowing the location of any of the coins, and pick a gold coin in one of the drawers. Now, what is the probability that the other drawer in the same cabinet contains a gold coin?

Solution (By Examveda Team)

Method 1:

If you have picked a draw with a gold coin, you must have (with equal likelihood) either:

1. Picked one of the gold coins in the cabinet with 2 gold coins
2. Picked the other gold coin in the cabinet with 2 gold coins
OR
3. Picked the gold coin from the cabinet with gold and silver

As these three possibilities are equally likely, and as the first two would mean the other draw contains gold, the *probability that the other drawer in the same cabinet contains a gold coin* is 2/3 or 66.66 %.

Method 2:

P(the other draw containing gold given that gold has been picked) = P(gold being picked and the other draw containing gold) / P(gold being picked) = (1/3) / (1/2) = 2/3

[This is just using rule that P(A given B)=P(A and B) / P(B)].