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## Money in Water

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #3265 Fun: (2.44) Difficulty: (2.19) Category: Probability Submitted By: cathalmccabe Corrected By: cowman12

You drop two coins into a muddy river by mistake. You saw one falling in, a 1 Euro coin. You know the other one had to be either a 1 Euro coin, or a 2 Euro coin.

After searching and pulling out one, and discovering it's a 1 Euro coin, what is the chance that the other is also a 1 Euro coin?

2/3

There are 3 possible combinations after you pull out a 1 Euro:

A 1 Euro was in the river initially, and you pull out the second one you saw fall in; therefore a 1 Euro is in the river still.
A 1 Euro was in the river initially, but you pull it out; therefore a 1 Euro is still in the river.
A 2 Euro fell in first, you pull out the 1 Euro you saw fall in; therefore a 2 Euro is still in the river.
These three states are all equally likely, so there is a 2 in 3 chance of pulling out a 1 Euro.

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