Question for the Math majors out there…
As I was driving back from the grocery store today, I saw a sign in a convenience store window that I had seen before. It says “we sold a winning lottery ticket.” I started thinking about whether that was a smart thing to advertise. On the one hand, some people might foolishly think that it’s a “winning store” and buy from them thinking they’re lucky or something. But on the other hand, others might avoid buying lottery tickets there because what are the odds that the same place will sell two winning tickets? And yet, it shouldn’t matter either way, because the probability that you will buy a winning ticket is completely independent of where you buy it, or what that store’s history of ticket sales is.
So here’s what I’m confused about: On the one hand, from a buyer’s point of view, whether a store has ever sold a winning ticket before shouldn’t have any bearing on their choice to buy there. Their odds of winning are exactly the same no matter where they go. Yet from the store’s perspective, the chance that they will sell two winning tickets in a given amount of time is far lower than the chance that they will sell one during that period.