The role of probability in solving the Monty Hall problem

[Jenny A]

No you shouldn't need to because the math makes the result obvious. But like all probability problems it can be demonstrated empirically. The more times you play the game the more obvious it will become that switching cards is the right answer. You can show that tossing two pennies results in one head and one tail in 50% of all two coin tosses by making a few hundred such two coin tosses. But the math will tell you that before you start. Similarly, if you play the three card game a few hundred times the experiment will vindicate the math.