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Given the child is 15 years old, it already knows about orbitals and the shape of a 1s-orbital as being spherical symmetric. Now over a large time, we look at the electron and note it’s distance from us every second or so. Sometimes the distance will be a bit closer, sometimes it will be a bit farther. At the end of large time frame, we calculate the average distance the electron was from our position. And this will be the time-averaged position of this electron.
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