Two players play a game on a special type of tree called a Fibonacci tree. Determine if the first player can win by strategically removing subtrees, one at a time.

The problem asks you to find how many pairs of numbers in an array are equal. Each index can only be part of one pair.

You're given an array representing weights. Implement a function to randomly pick an index from the array, where the probability of picking each index is proportional to its weight.