A game is played as follows. There are 2 goats and 1 car, each hidden behind...

A game is played as follows. There are 2 goats and 1 car, each hidden behind a numbered door. You choose a door (for simplicity you always choose door 1) and then Monty Hall opens one of doors 2 or 3.The door that he opens always reveals a goat. Now Monty offers you to switch yourchoice of doors

(a) What is the probability that you win the car by switching your choice? Hint: Consider the events {Ci= car is behind doori} and use the first Bayes formula

(b) Explain the paradoxical result from part (a). Why is it >1/2?

(c) Now suppose that if Monty has to choose between opening doors 2 or 3 (i.e.the car is in door 1), he chooses door 2 with probability p ≥ 1/2. What is the probability that the switching strategy wins the car given that Monty opened door 2?Hint: Let D2 be the event that Monty opens door 2, then P (winning|D2) =P(C3|D2). Now apply the second Bayes formula.

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orchestra answered 1 year ago

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