Assume the sink on the left has a soap dispenser that never works, but a tap that always works. The sink in the middle has a soap dispenser that always works, and a tap that always works, but because they both work, the dispenser is out of soap fifty percent of the time. The tap on the right has a soap dispenser that always works, but a tap that never works.
Given those criteria, what are the odds that you will see somebody emerge from one of the stalls after noisily vacating their bowels, give their hands a quick sniff and then head out the door without making an attempt to wash their hands.
Bonus points if you can calculate how many times the left urinal will spontaneously flush while this is going on.
Show your work.