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. Prove that the expected value of this game is greatest when you always switch. Include a full mathematical explanation of all probabilities.
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. Prove that the expected value of this game is greatest when you always switch. Include a full mathematical explanation of all probabilities.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. Prove that the expected value of this game is greatest when you always switch. Include a full mathematical explanation of all probabilities.
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