Monty Hall
A game show has three doors. Behind one is a car; behind the other two are goats. You pick a door. The host, who knows where the car is, opens one of the other two doors to show a goat, then offers you the chance to switch.
Should you switch? What are your chances each way?
Show hint
What was the chance that your first pick was wrong? The host never reveals the car.
Show solution
Switch. Sticking wins 1/3 of the time; switching wins 2/3.
Your first pick is wrong 2/3 of the time. In those cases the host must open the only other goat door, so the remaining door is the car. Try it: simulating 10,000 games in Python is a nice ten-line exercise.
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