The Monty Hall Cash game costs $12 to play. Once you pay, you have a choice of three doors. Behind one door is $20, behind the other two is absolutely nothing (i.e. $0). You pick a door, say number 1, and the host running the game, who knows what’s behind the doors, opens another door, say number 3, which has absolutely nothing. He says to you, “Do you want to switch to door number 2?”. You can decide to switch doors, or stay with your initial choice. You “win” whatever is behind the door you end up choosing. Use a python Jupyter notebook to run simulations of the game to estimate/approximate the expected value of the game if you always switch, and the expected value if you always stay. OR: Prove that the expected value of this game is greatest when you always switch. Include a full mathematical explanation of all probabilities (no “hand waiving”!) and include any references or sources.
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The Monty Hall Cash game costs $12 to play. Once you pay, you have a choice of three doors. Behind one door is $20, behind the other two is absolutely nothing (i.e. $0). You pick a door, say number 1, and the host running the game, who knows what’s behind the doors, opens another door, say number 3, which has absolutely nothing. He says to you, “Do you want to switch to door number 2?”. You can decide to switch doors, or stay with your initial choice. You “win” whatever is behind the door you end up choosing.
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Use a python Jupyter notebook to run simulations of the game to estimate/approximate the expected value of the game if you always switch, and the expected value if you always stay.
OR:
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Prove that the expected value of this game is greatest when you always switch. Include a full mathematical explanation of all probabilities (no “hand waiving”!) and include any references or sources.
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