Ada has 14 coins, numbered 1 to 14. Each coin has exactly one face called "heads". When flipped, coins 1,2,3, ...., 13,14 heads with probabilities h1, h2, h3, ...., h14, respectively. When Ada flips each of the 14 coins exactly once, the probability that an even number of coins land heads is exactly 1/2. Must there be a k etween 1 and 14, inclusive, for which hk = 1/2? Prove your answer.
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