Around 2 million people visit Mt Rainier National Park every year, hundreds of thousands of which go on hikes. Of the 2 hikes I've done at Rainier in recent years, I've been within 50m of a black bear once. While a very small sample size, anyone who hikes here will tell you it's very common to see one. Never, in the history of Mt Rainier National Park (est. 1899), has anyone been attacked by a black bear. Based on that, I'd put the chance closer to 1 in 10 million or so.

Ooooh! Thank you! That's some interesting data! Even if record-keeping was worse 50+ years ago and hiking was less popular because fewer people had the time for it, that still puts it easily at 1 in 1 million, still beyond the ranges I considered when I created the question. :-o

Where is the hypothetical encounter at? The black bears you find in Florida are pretty tiny and timid, but one you meet in e.g. Vermont is probably somewhat more dangerous.

@AndrewHartman Oh! Does it make an order-of-magnitude difference? I'd guess Alaska is probably a good place to pick because I might post the same poll for grizzly bears (and maybe polar bears), and Alaska could be the place for all polls, making them more comparable.

@DawnDrescher If you're not excluding Florida it definitely makes an order of magnitude difference. I think if you exclude Florida specifically then it's probably not as dramatic?

Reminds me of the kid who wanted to hug the beeeeear