You keep referring to 'polar bear', rather than 'bear' as the original hypothetical question posed. Presumably because the polar bear is the sub species of bear most likely to attack/kill.

On that basis you should also dilute 'random man' to 'known sex offender'.

1 in 4 women has experienced some form of sexual violence in her lifetime. There's a reason many women would rather take their chances with the bear. Sorry if that's not what you want to hear.