What are the chances that 3 months into pregnancy, you still do not know it without taking a test?

"Know" in what way? The vast majority of women will have missed several periods and been motivated to take a test or visit their doctor well before 3 months.

And certainly, even before the availability of pregnancy tests, most women would have strongly suspected, well before 3 months, that they were pregnant.

But I suppose it's possible for a woman who has very infrequent or irregular periods, and has been carefully using contraception (and so would have no reason to suspect pregnancy), to have few or no other symptoms, and so not recognize that she might be pregnant.

(I knew a woman who didn't find out until around 5 months -- she was breastfeeding and hadn't had a period, and had no real pregnancy symptoms.)

I used to disbelieve those stories about the mother "not knowing" until a month or a week before she gave birth. But the daughter-in-law of a good friend of mine gave birth at less than an hour's notice, she not having known that she was pregnant. My friend is a sensible middle-aged woman who is not prone to exaggeration - she had to call an ambulance and then help her daughter-in-law give birth in the ambulance outside the hospital - no time to transfer the daughter-in-law into the hospital.