Suppose you\'re on a TV game show, and you\'re given the choice of three doors.

Question

Suppose you're on a TV game show, and you're given the choice of three doors. Behind one door is a brand new car, behind the others, nothing. You pick a door. The TV host, who knows what's behind the doors, chooses another door and opens it to show you that it has nothing. Should you change your decision? Don't think about this too deeply just yet. Do you feel (intuit?) that you should change your choice? Answer initially without researching the question. What is the thinking behind your answer? Conduct a survey of ten of your friends/colleagues to give their opinion. You may wish to provide them with a copy of the question. Include in your answer a table setting out the results of this survey. Also create a simple chart with Excel to present the results of your survey.

Explanation / Answer

A.i. I feel, I should not change my choice.

2. Most people will say that it makes no difference,I swap or not. Behind one closed door is nothing and behind the other closed door is a car,therefore, the chance of choosing the car is 50|50,So it makes no difference I swap or not. This sounds perfectly sensible however its not correct. The Monty Hall problem is a puzzle about probability,simple to understand but the answer is counter-intuitive.The answer is I should always swap, this gives twice the chance of winning the car.The simplest way to explain this is to examine what my chances of winning the car are for the two strategies swapping and not swapping.

Lets start by choosing not to swap, at the start of the game I am asked to pick a door since there are three doors and only one hides the car the probability of me picking the door is 1/3 or about 33% and since there are two empty doors the probability of me picking nothing is 2/3 or about 67%.

Now if I dont swap the door it does not matter which of the both doors the host opens because I am sticking with my first choice and the chance that I already pick the car is 33%. And the chance that I have already picked nothing is 67%. So by not swapping i have 33% chance of winning the car and 67% of winning nothing.

Lets look at the consequences of swapping, if by luck i pick a car 1st time(33%chance) so if I swap I will get nothing. So if I swap I am going to win nothing atleast 33% of time, what about I pick nothing ,this time there is only one door that has nothing and the host has revealed and I open the only other closed door i.e. a car infact every time I pick a empty door and swap I will win a car and the chance of picking a empty door 1st time is 67%. So, by swapping I have 67% chance of winning a car and 33% chance of winning nothing.So i should always swap to the remaining door because it doubles the chance of winning the car.

Marilyn vos savant advocates swapping the door while most of the mathematicians believe that it makes no difference we swap or not.

Barry Pasternack, Ph.D.,California Faculty Association said "Your answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem."

W. Robert Smith, Ph.D.,Georgia State University said "I am sure you will receive many letters on this topic from high school and college students. Perhaps you should keep a few addresses for help with future columns."

Seth Kalson, Ph.D.,Massachusetts Institute of Technology said "You are indeed correct. My colleagues at work had a ball with this problem, and I dare say that most of them, including me at first, thought you were wrong!"

At last Marilyn vos Savant said "We've received thousands of letters, and of the people who performed the experiment by hand as described, the results are close to unanimous: you win twice as often when you change doors. Nearly 100% of those readers now believe it pays to switch."

Survey of my 10 friends/colleagues NAME CHOICE CHANGE OR NOT Sam Change Jack No Change Harry No Change James Change Jacob Change Kai No Change Josh No Change Patrick Change Eli No Change Neil Change

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