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?

## 11 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.

Loving this blog, great content and will be coming back to find out more for sure!

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