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Solve the Monty Hall problem in the case of 4 doors (3 goats, 1 car, host opens 1 door after your initial selection), using Bayes'

"Solve" the Monty Hall problem in the case of 4 doors (3 goats, 1 car, host opens 1 door after your initial selection), using Bayes' Rule. Assume a uniform prior distribution; provide sufficient detail and argue why it is either advantageous to stay or switch your initial selection following the reveal.

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