I'm curious how people work through this problem.
You are the general of an army of essentially infinite numbers. The opposing general has an army equally as massive. There are three battlefronts that will decide the war. A battlefront is won if you send as many or more troops than the opposing general and lost if you send less. To win the war you must win two of the three battlefronts. You sent your troops to the battlefronts in the magnitudes of 1/4 : 1/4 : 1/2 of your total army. The opposing general uses no strategy and distributes his troops randomly. What is the probability that you win the war?