I drew a decision tree once to show all possible states, with the 1/3 and 2/3 probabilities along each edge, which finally made it click for the coworkers I was

I drew a decision tree once to show all possible states, with the 1/3 and 2/3 probabilities along each edge, which finally made it click for the coworkers I was trying to convince. In the tree it becomes blindingly obvious that the probabilities are.