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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