You are on a game show and have made it to the “Final Showcase.” - Congratulatio

ID: 3173053 • Letter: Y

Question

You are on a game show and have made it to the “Final Showcase.” - Congratulations. You are to pick one of three doors, behind which will be your prize. Behind one door is a new Ferrari and a degree, behind the other two doors are mildewed cheeses. After you select a door (for example, door # 1), the host shows you another door (for example, # 2) and there is cheese behind it (he always shows you a cheese because he knows where the prizes are). The host offers you the chance to switch to the third door or keep the one you originally selected, what should you do? (Support your strategy).

Explanation / Answer

This is a case of a Monty Hall Problem. We will solve it in 2 ways

Solution -1:

The best way to solve such a problem is by taking all the 3 possible combinations: The given table is from the perspective of the person who choses door-1 and it gives all the 3 combinations which are possible for the cheese and the prize.

Clearly from the above table we can see that in case the person switches the door after the host opens up a door behind which there is cheese , in 2 out of 3 cases he will win the prize and therefore ther person should switch to the third door after the host opens up a door behind which there is cheese.

Solution -2: The intuitive solution behind this problem is that if the person choses the door initially which has cheese behind it then the host would open the door with another cheese and so switching will make the peron win the prize. This has a probability of 2/3 because the person choosing a door with cheese behind it has a probability of 2/3.

Similarly if the person choses the door with prize behind it then switching the door will make him lose but this has a probability of only 1/3

Therefore it is better for ther person to switch once the host opens up a door with cheese behind it.

Door-1 Door-2 Door-3 If door chosen is switched If door chosen is not switched Prize Cheese Cheese Lose Win Cheese Prize Cheese Win Lose Cheese Cheese Prize Win Lose

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You are on a game show and have made it to the “Final Showcase.” - Congratulatio

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