Explanation of the Let's Make a Deal Problem

You picked door 1. Monty eliminated door 3 (that's your evidence). What is the chance that the car is behind door 2 (so your hypothesis is "The car is behind door 2")?

Start with 300 situations in which you picked door 1.

In 100 of those, the car is behind door 2. In each of these, Monty eliminates door 3, because he can't eliminate the door you picked (1) and can't eliminate a door with a car behind it (2).

In 200 situations, the car is not behind door 2. It is behind door 1 in 100 situations, and behind door 3 in 100 situations. In the door 1 situations, Monty can either eliminate door 2 or door 3 (since you didn't pick either of those, and neither has a car behind them). Assuming he chooses randomly, he'll eliminate door 2 50 times. In the door 3 situations, Monty can't eliminate door 3 at all, because it has a car behind it.

So, there are 150 situations in which Monty eliminates door 3. In 100 of these, the car is behind door 2. So the chance of getting the car if you switch to door 2 is 2/3 (and the chance if you stay with door 1 is 1/3).