This isn't a homework problem. It's actually derived from thinking about how much police can give citizens the benefit of the doubt when it comes to whether someone is reaching for a weapon or reaching somewhere for a different reason.
If there's a 5% chance that someone is reaching for a gun in ambiguous situations, what is the chance that the police person will have a gun drawn on them if they allow people to reach for something in 20 different situations?
My initial thinking was near 1, but not 1.
What I'm not sure about is an actual, systematic answer.