Monty Hall Problem

The Monty Hall problem is when you have three choices and one of the choices has a prize behind it and you are told to pick one of the three options. After you choose your option the person will show you one of the options that doesn't have a prize. They will then allow you to either keep your first choice or change your choice to the other option.

When i played the game 10 times and stayed with my first choice i won 5 of the ten times and lost 5 of the ten times. Therefore i had a 50% chance of winning.
When i played the game 10 times and switched my choice i won 8 of the ten times and lost 2 of the ten times, allowing me to have an 80% chance of winning.
With these results relating them back to myth busters they are very similar because in myth busters whenever they switched their door they won more often then when they kept it the same.

After we played it ten times each we had to run a test of 1,000 times for each.
When we kept our choice during the 1,000 times. 34% of the time they won and 66% of the time they lost.
When we switched our choice during the 1,000 times 65% of the time we won and 35% of the time they lost.
Relating this back to myth busters this also helps prove the theory that when you switch your choice you have a better chance of winning.

My own thoughts about the Monty Hall problem is when I first heard what it was I thought there's no way thats possible because each choice has a 50% chance of being chosen. My first thought was this myth will be busted. Once they started running tests i was stunned at the results i was seeing. I was very surprised that they were right and that when you changed your choice you have a better chance of winning. I believe people stay with their first choice because of two reasons, either they like sticking with their gut feeling or they figure why change each has a 50% chance of winning because they don't know the whole truth about the numbers. Another game show that I think would be interesting is the game deal or no deal. You could analyze the same thing when it gets down to the last case to see if they stick with their first choice or switch the cases.