The mean of means (of state e) is close to .36. If you take .3 * .36 + .4 * (1-.36), you get .364, so this seems to make sense. Note that I’m weighting the switching to e percentage based on the percentage of being in that state in the first place.
The Monty Hall Problem is famous in the world of statistics and probability. For those struggling with the intuition, simulating the problem is a great way to get at the answer. Randomly choose a door for the prize, randomly choose a door for the user to pick first, play out Monty’s role as host, and then show the results of both strategies.
The numeric output will vary, but look something like: