Problem #5 The cartoon on the opening slide of this week\'s lecture demonstrates

Question

Problem #5 The cartoon on the opening slide of this week's lecture demonstrates the famous 'Monty Hall Problem'. This is a famous statistical puzzle. Go online and read up on the game and explanations on why the user should switch. Then describe why the user should decide to switch doors. A key point to remember is that the game host is tequired to pick a door behind which is a goat. That is, the host will never pick the winning door. This problem is very interesting for all kinds of reasons, one of which is the fact that intuitively, most people (including many mathematicians) would say that it really isn't necessary to switch. And yet, your likelihood of winning most definitely does improre if you switch. Math and statistics can be very interesting when it comes to these sorts of things Note for problem #5 I do NOT want you to simply paraphrase. I want you to think about the problem and show that you understand the reasoning behind why the user should switch. Then simply write it out in your own words. * Your response does not have to be long A single paragraph is ust fine

Explanation / Answer

When the player makes his first choice, he doesnt know behind which door car is and hence, he will make a random pick from 3. So, his probability of winning a car is 1/3.

Then the host, who knows behind which door the car is, will open a door behind which there is a goat. So, the host intentionally eliminates one wrong choice for the player. At this point, when the player makes a switch, he is making a pick from the available two options and hence, the probability of winning is 0.5. But if he stays with his original choice, his probability will remain as 0.33.

Here, the increase in probability is from the additional information provided by the host opening the door with a goat. Once this information is available, your number of choices reduces and then if u make a choice, you have 50% probability to win the car.

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