Saturday, April 12, 2008

Switch!!!

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

upon knowing the scenario and putting myself as a contestant, without google being my sidekick, i tried to reason it logical. let's say the scenario as happened as mentioned above, then that would leave me to a 50%-50% chance of getting the car, so why switch? don't be so fickle minded and have faith in your choice, follow your gut, follow your heart! so my decision was NOT to switch.

is that your final answer? door 1?

YES DOOR 1! OPEN!!!

unfortunately, my reasoning is wrong. to switch would be to my advantage. and this is known as the monty hall problem, named after the host of the american game show which this puzzle is loosely based on. even after reading the rationale behind the reason for switching, i wasn't really convinced that it would be more advantageous to me and i pondered about for the entire day. from work, to home and to the toilet. but i guess this picture says it quite well. 



the most misleading rationale one would make is the fact that after the host reveals one goat, it's a 50%-50% chance of getting the car. conversely, your chance is only 1/3. as it's based on your initial decision when you had to choose 1 out of the 3 choices. showing you the wrong door, doesn't increase your chance to 1/2. to exaggerate and make it more obvious. imagine 100 doors, with only 1 with a car behind. by you picking door 1, and the host opening 98 doors that have goats in them, does that mean it's 50%-50% probability that you have the car when you don't switch? in the 100 door scenario, i WILL switch! that would give me a 99% probability of getting the car! 

so would you still switch? ;)

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