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**Quick** Let's play the shell game. I mix up three identical shells, one has a ball under it. You choose a shell. Instead of showing you your shell, I lift up another one that I know doesn't have the ball. You then get to pick which shell you'll take. What is the probability that the ball is under your original shell.

Now I say the answer is 50%

However, my statistics book says the answer is 33%, because there was a 33% chance the ball was under the first one you chose. (which I see why that would be an opinion but I don't agree with it cause it seems like the choices are independent)

What's your opinion?