You have two coins that look identical, but one of them is fair and the other is weighted. The weighted coin has a \( \frac{3}{4} \) chance of flipping heads and a \( \frac{1}{4} \) chance of flipping tails.

Unfortunately, you've forgotten which coin is which! You decide to keep flipping them together, one in each hand, until you get a flip where one coin shows heads and the other shows tails. Then you'll assume that the coin showing heads is the weighted coin. **If you do this, what's the probability you'll correctly identify the coins?**

Good luck, this is a very tricky question! Remember that a fair coin is one that has a \( \frac{1}{2} \) chance of flipping heads and a \( \frac{1}{2} \) chance of flipping tails.

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