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Monty Hall Problem Probabilities:
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The Monty Hall problem is a probability puzzle based on the American TV show "Let's Make a Deal." It demonstrates that switching doors after one is revealed increases your chances of winning from 1/3 to 2/3, which is counterintuitive to many people.
The calculator demonstrates the probabilities:
Explanation: When you first choose a door, you have a 1/3 chance of being right. The host then reveals a non-prize door, and switching essentially means you get the combined probability of the two remaining doors (2/3).
Details: This problem is famous for showing how human intuition about probability can be wrong. It's used in probability education to demonstrate conditional probability and the importance of updating probabilities when new information is revealed.
Tips: Select your strategy (stay or switch) and the number of simulations to run. The calculator will show both the theoretical probability and empirical results from simulations.
Q1: Why does switching give better odds?
A: Because your initial choice has only 1/3 chance of being correct, so switching gives you the remaining 2/3 probability.
Q2: Does this apply to any number of doors?
A: The effect is more pronounced with more doors. With N doors, staying gives 1/N chance while switching gives (N-1)/N(N-2) chance.
Q3: What if the host doesn't know where the prize is?
A: The probabilities change if the host might accidentally reveal the prize. The classic problem assumes the host always reveals a non-prize door.
Q4: Why do people find this counterintuitive?
A: Humans often think probabilities should be 50-50 after one door is revealed, neglecting that the host's action provides additional information.
Q5: Are there real-world applications?
A: Yes, in any situation where you get additional information after making an initial probabilistic choice (e.g., medical testing, game theory).