There are 3 bags. One contains 2 gold coins, another has 2 silver coins and the 3rd has one of each.
You pick a bag at random, and without looking inside take out one coin. It's gold. What is the probability that the other coin in that bag is also gold?
posted by steven | 1:24 PM
10 Comments:
2/3.
As there are three gold coins, there's a 2 in 3 chance that you picked one of the gold coins from the bag with two gold coins, and a 1 in 3 chance that you picked a gold coin from the bag with 1 gold and 1 silver coin. Therefore there is a 2/3 chance that the other coin is gold.
I thought the question was more ambiguous: "What was the probability, given that you have picked a gold coin?" Doesn't that lead to 1/2?
What Anonymous November 19 said.
Hi,
I thought the question was more ambiguous: "What was the probability, given that you have picked a gold coin?" Doesn't that lead to 1/2?
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If I'm understanding this correctly, the probability is still 2/3. The probabity that you pick silver isn't the same that you pick gold. The fact that you already picked gold means that there is a 2/3 chance you picked from the gold/gold bag and therefore that the other coin is gold (if you picked from the gold/silver bag, the other coin is silver - this is a 1/3 probability).
Hope this explains it.
1/2
I agree with Steven.
There are 3 gold coins to choose from and 2 of them lead to a second gold coin.
Here is another way to state the problem: You picked a gold coin. What is the chance that you picked from the bag that has 2 gold coins? Since there are 3 gold coins total, there's a 2/3 chance you picked from the bag with 2 gold coins.
1/3
there is only one bag with 2 gold coins, therefore the question is asking what is the probability of getting that bag.
1/3
there is only one bag which culd possibly contain anothr gold coin
Thank you! I didn't know they picked up on it until I saw your comment.
Of course it is 1/2! There are only 2 possibilities left. It is clear that you either have the bag with 2 gold or the bag with 1 gold and 1 silver. The 2 silver coin bag is out of the question.
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