How many hidden Jews amoung us?

I am not a Jew, but I have a question in mind. Judaism is 4000 years old, isn’t it? To be a Jew, you need a Jewish mother, and you automatically become a Jew. Isn’t that the case? My question now is: are all people Jews? Think about it—even if you deny it, you’re still a Jew. It’s just a matter of time before the Jewish “seed” reaches every female, and then the whole world is Jewish. The question now, using statistics (overly simplified), is: how many hidden Jews are among us? Let’s take the worst-case scenario and assume the fertility rate of Jews is the same as in today’s Israel, around 3 children per woman, which is 1.5 females per mother. Every generation (33 years), there’s a 1.5× increase in females. Over 4000 years, that’s about 4000 / 33 ≈ 121 generations. 1.5¹²¹ ≈ 10^21. Assuming we started with only one woman, she is by now very likely (>99.9%) the ancestor of all humans. (Again, I know this is oversimplified.) Now back to the very start: I’m not a Jew… or am I? I’m most likely a Jew—no, wait—I must be a Jew because probably some great-grandmother of mine was one. I know that sounds stupid, but I can’t quite put my finger on what exactly is stupid.