Say I have 3 colored cubes. 1 is white (the control-object), 1 is red, 1 is blue. I will scoop up all 3 cubes and drop them from my hand into a box top. What is the probability that the Blue cube will fall closer to the White cube than the Red cube does?
Additionally, I'm trying to determine how to increase/decrease the difficulty of achieving a result of the Blue cube being closer to the White cube when the Blue and/or Red cubes are increased in quantity.
Basic approach. Call the three cubes white, $A$, and $B$. That is, we pretend we don't know which one of $A$ or $B$ is red, and which one is blue; either case is equally likely. Under one of those cases, the condition is satisfied, and under the other, it is not. Therefore, the probability in question is...?