Is it OK to Probably Injure Traffic Blocking Protester to Possibly Save Life?

Let's be explicit so everyone is on the same page. This is unfortunately not a purely hypothetical question except for the preciseness I am hypothesizing.

You are driving your mother to the hospital along a route that you have every reason to believe is clear. But it's not, because of a protest. A protest that would not legally be allowed to totally block traffic as they are doing. Because of cars stopped behind you, the protest adds 20% to the probability your mother will die. If you slowly plow through the protest, there is an 80% chance that you will injure someone fairly seriously but no chance you will kill somebody. Are you wrong to do that? Should it be illegal? Does it matter what the protest is about?

(I think most of you will say it's OK. To those that did, what if the mother death probability went up by only 5%, the protester death probability went from zero to 70% and the policy being protested was clearly bad?)