https://www.janestreet.com/puzzles/current-puzzle/
For a fixed p, independently label the nodes of an infinite complete binary tree 0 with probability p, and 1 otherwise. For what p is there exactly a 1/2 probability that there exists an infinite path down the tree that sums to at most 1 (that is, all nodes visited, with the possible exception of one, will be labeled 0). Find this value of p accurate to 10 decimal places.
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