Bertrand's Box Paradox
Two boxes sit in front of you. Box 1 contains one $\
$ bill and one $\$5$ bill. Box 2 contains two $\
$ bills.
You pick a box uniformly at random, then draw a bill from it at random. The bill you drew is a $\
$ bill.
What is the probability that the second bill in your chosen box is also a $\
$ bill?
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