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 its a 1 euro coin, what is the chance that the other is also a 1 euro coin?
There are 3 possible combinations after you pull out 1 euro:
A 1 euro was in the river initially, and you pull out the second one you saw fall in; Therefore 1 euro is in the river still A 1 euro was in the river initially, but you pull it out; Therefore 1 euro is still in the river 2 euro fell in first, you pull out the 1 euro you saw fall in; Therefore 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 1 euro
Today's brain teaser courtesy of Braingle.com.