The rule is: There's no such thing as absolute security!

But let me explain some facts: since the beginning of record of accidents concerning bears 85 years ago, 19 people have been killed. Nine of them were hunters who wanted to kill the bears and I want to remove that group from this statistic. In addition, hunting in Katmai National Park has been permitted since then. So there are 10 fatal accidents left but two of them occured just in 2003. In these 85 years many more people died because of bees, moose and other people. Nobody is afraid of dying from the effects of a bee sting or that he/she will be killed tomorrow, but we are nurtured to be afraid when seeing a bear.
Do you want to know what is statistically the most dangerous part of the bear watching tour to Alaska? It is the car ride to the airport!
But of course I will take your fears seriously and we will talk in detail of how to behave in bear territories and I will refer to literature.
Another fact: As far as I know, a bear has never been attacked a group of at least three people worldwide!

My advice: Continue being anxious and thereby careful and you will fully enjoy the brown bear encounters.

In bear territory there are plenty of behavioral measures and rules to follow. I will thoroughly prepare you for these!
WE are visiting the bears. Respect and dignity for nature and especially for the brown bears are indispensable!
This protects both the bears and us!