Paul, a very daring guy, decides to go to a volcano.

He needs to decide between $$10$$ volcanos. The first one has a probability of $$\frac{1}{2}$$ of erupting. (While Paul is there) The second one's probability of erupting is $$\frac{1}{4}$$. Each following volcano's probability of erupting is $$\frac{1}{2}$$ of the previous one. (So the next one would be $$\frac{1}{8}$$). If Paul decides randomly which volcano he wants to go to, what is the probability that the volcano erupts while he is there? Express your answer has a decimal to the nearest thousandth.

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