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Notes -
I would expect being alone would massively increase the risk rate. How many people would steal a stack of bills if they were left out in the open but there are people all around who knows they don't belong to the thief, vs how many would steal the stack of bills if they had total anonymity?
But the risk rate is probably 0.000001 or something like that so even with a massive adjustment hard to get to 1%
I can't pretend to know the exact numbers, but I think you're vastly underestimating the danger men pose women, and the numbers can shift truly massively. I think a lone woman walking through a busy mall in day time is almost certainly will not experience any violence. There is a slim chance, there are some mentally ill psychos out there who randomly assault women, but it's neglible.
Meanwhile, I think the odds of a lone woman walking through certain Chicago streets at night is almost certain to experience violence. Far greater than just 1% at least, despite how low her odds were around dozens of men in the mall.
Being in a random forest with a truly random man would be somewhere in between those. The man, on average, would probably be worse than the men in the mall, since a random man could be a guy in jail or a 3rd world militant, but also is probably better than the men hanging out on the Chicago streets at night. Both of them being alone would be in between the woman being surrounded by civilized strangers in a mall and the man's criminal buddies on the street too. I'd give somewhere between 0.1-5%, personally, of being assaulted.
So if I was a woman, I'd probably take a man over a black bear, but not other types of bears.
But part of the problem with Chicago is you are likely to encounter a number of men (ie there isn’t just one person). So your theory could be correct but your odds per encounter is still probably overstated.
You also ignore age. Is the guy 40? 50? 30? That needs accounted for.
You have to account for damage per attack. Even if you are right, the woman has a much better chance against the dude then a fucking bear.
Finally, I think the 1% bear attacks is grossly misleading. The fact pattern here necessarily suggests the man or bear is very nearby. That, coupled with the lack of expertise with bears, greatly increases that 1% figure.
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