This was exactly how I got introduced to D&D.From what I've seen among the players in my area, almost none had a story as simple as "I saw the rulebook in the store and decided to buy it".
I was eight (this was in 1981) or nearly so, and in a hobby store near my grandmother's house, I saw the shiny red Basic D&D boxed set. There was a picture of a dragon on the front, which was super-cool to eight year old me. So, with allowances saved for many moons, I bought it.
That summer, myself, my brother (11) and three neighbor kids (of approximately those same ages) learned and took turns running the game.