2.1 Monty Hall for N doors (10 pts) You are a contestant at a show with N closed

Question

2.1 Monty Hall for N doors (10 pts) You are a contestant at a show with N closed doors where N >3. One of the doors has a car and all the others have no prize. You first pick a door at random. Then, the host picks a door uniformly at random among the remaining doors that have no prize in them and opens that door for you. You then face the choice of sticking with your initial selection or switching to one of the remaining closed doors uniformly at random? How should you play? Justify your answer with rigorous probability calculations.

Explanation / Answer

Solution:

I would switch the choice given the chance after 1 door is exposed with no gift.

Explanation:

Because of variable change, previously it was 3, and now it is 2.

So when the offer is to choose one door out of the 3 the probability of hitting a gift is 33.33%, but after one of the door is exposed with no gift then after switching the choice the probability to hit the gift become 66.66%.

Based on this the probability is getting increased so it is wise to change the choice.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

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