# Question: 2 more monty hall lets consider another variation of the...

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2 More Monty Hall

Let’s consider another variation of the Monty Hall problem, however, instead of 3 doors there are four doors. Behind one door is the prize, and behind the other three doors is nothing. Say the doors are labeled A, B, C, and D. Suppose that Monty Hall always opens the earliest door possible (the door whose label is earliest in the alphabet) with the restriction that he can neither reveal the prize nor open the door that the player picked. This gives contestant Mergatroid, an engineering student from Waseda University, just a little more information about the location of the prize. Suppose that Mergatroid always switches to the earliest door, excluding his initial pick and the one Monty opened. What is the probability that he wins the prize?