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The Drunkard's Walk, How Randomnes Rules Out Lives, by Leonard Mlodinow
chin:
My daughter read a book about math for kids, kind of like a funny version of the Story of Math & Mathematicians, and it offers an even more simple solution of the birthday problem.
Let's say in the case of 30 people, you line them up on a straight line, and start counting from the left.
The 1st one would have no chance of having the same birthday as the person on the left, since there is no body on the left; The 2nd person would have 1/365 chance having the same birthday as the one single person on the left; then the 3rd person would have 2/365 since there are 2 person on the left; and so on.
At the end, you add up from 0/365 ... to 29/265, or 29*15/365.
chin:
--- Quote from: wongyan on 31 October 2009, 14:32:31 ---Let's say,
you play Sik-Bo in Casino.
After four SMALLs in a roll, engineering/scientists mind-set will always say the next game is 1/2 Big, 1/2 Small. While some other people will start to believe the dice are biased and the chance of SMALL is higher on the next game. So everything may come to an art. I believe Chin will agree also. No matter how accurate you model your wagering system, the assumptions behind are all set by human.
Let's get back to the three doors dillemma. I will look into the host's eyes and say "Yes..............Maybe" and see if any clue from his eyes or his facial expression can tell. Besides, I may also knock on the door and see if the goat bleats. (Probability tells no difference)
--- End quote ---
The probability actually changed in the 3-door problem after the host open an empty door.
What you suggested is a but similar to in horse racing, some gamblers would guest the trainer intention, etc...
kido:
--- Quote from: wongyan on 31 October 2009, 14:32:31 ---Let's say,
you play Sik-Bo in Casino.
After four SMALLs in a roll, engineering/scientists mind-set will always say the next game is 1/2 Big, 1/2 Small. While some other people will start to believe the dice are biased and the chance of SMALL is higher on the next game. So everything may come to an art. I believe Chin will agree also. No matter how accurate you model your wagering system, the assumptions behind are all set by human.
Let's get back to the three doors dillemma. I will look into the host's eyes and say "Yes..............Maybe" and see if any clue from his eyes or his facial expression can tell. Besides, I may also knock on the door and see if the goat bleats. (Probability tells no difference)
--- End quote ---
I also agreed with wongyan, without further thinking, 50-50 was my answer and switching doesn't make any difference. But it was so tempted to wiki the term and the result was so surprised. (I should have know this problem should have odd results because it shouldn't be that trivial since Chin specifically posted it here.) ::)
hangchoi:
Me too. Trapped by the Monty Hall problem......... :)
hangchoi:
Yan,
If you want to visualise the Monty Hall Problem, here you go:
http://www.youtube.com/watch?v=mhlc7peGlGg
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