Document1 Word Draw Design Layout References Mailings Review View Help Tell me w

Question

Document1 Word Draw Design Layout References Mailings Review View Help Tell me what you want to do You are a contestant on a quiz show. There are 3 doors. The quiz master tells you that behind one of the doors is cash prize of $1,000,000 dollars. Behind the other two doors is a goat. You select door 1 and before he shows you what is behind door 1 he opens door 2 and shows you a goat. Then he asks you," would you like switch to door 3. What is your decision? Use a tree diagram to explain your answer

Explanation / Answer

This is an example of a Monty Hall's dilemma. In this case the contestant should definitely switch the door, because it makes his winning chances percentage double. Consider the table below:

So we see that if we switch we have a 67% chance of winning, as compared to 33% if we don't switch.

The trick here is that once the contestant chooses door 1, and the prize is behind door 2, so the host must open door 3, he has no other option. This is what increases the contestant's winning chances.

Door 1 Door 2 Door 3 Staying at 1 Switching to 3 Goat Goat Prize Wins goat Wins prize Goat Prize Goat Wins goat Wins prize Prize Goat Goat Wins prize Wins goat

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