Flipping Coins and Independence

An experimenter has two fair coins and one biased coin. The biased coin lands on heads with probability 3/4.

The experimenter randomly selects one of the three coins and flips it until they get heads.

Let \(A\) be the event that the experimenter flipped the biased coin.
Let \(B\) be the event that it took the experimenter an even number of flips to get heads.

Are events \(A\) and \(B\) independent?

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