1. What is the Monty Hall Problem?

The Monty Hall problem is a probability puzzle based on a game show scenario. You're given the choice of three doors. Behind one is a car (prize) and behind the other two are goats. After you pick a door, the host opens another door revealing a goat, then offers you the choice to either stay with your original pick or switch to the remaining unopened door.

2. How Does the Calculator Work?

The calculator uses the Monty Hall probability formula:

Where:

• \( P \) — Probability of winning
• \( \text{switch win} \) — Strategy of switching doors
• \( \text{host opens goat} \) — Host always reveals a goat

Explanation: Switching doors gives you a 2/3 chance of winning, while staying with your initial choice gives only a 1/3 chance.

3. Importance of Probability Calculation

Details: Understanding this counterintuitive probability concept helps in decision-making scenarios where new information becomes available after an initial choice.

4. Using the Calculator

Tips: Select whether your initial choice was the car or a goat, and choose whether you would switch or stay. The calculator will show your probability of winning.

5. Frequently Asked Questions (FAQ)

Q1: Why is switching better?
A: Because there's a 2/3 chance you initially picked a goat, so switching would then get you the car.

Q2: Does the host's knowledge matter?
A: Yes, the host must always know what's behind the doors and always reveal a goat.

Q3: What if there are more doors?
A: With more doors, the advantage of switching becomes even greater.

Q4: Is this just theoretical?
A: No, actual experiments and simulations confirm these probabilities.

Q5: Why is this counterintuitive?
A: Because humans tend to think the probability becomes 50-50 after one door is revealed, ignoring the initial probabilities.