BTW, I'm not referencing a school book. It's just a book on statistics.
Let's play the shell game. I mix up three identical shells, one has a ball under it. You choose a shell. Instead of showing you your shell, I lift up another one that I know doesn't have the ball. You then get to pick which shell you'll take. What is the probability that the ball is under your original shell.
Now I say the answer is 50%
However, my statistics book says the answer is 33%, because there was a 33% chance the ball was under the first one you chose. (which I see why that would be an opinion but I don't agree with it cause it seems like the choices are independent)
What's your opinion?
I am too lazy and bored to keep explaining the Monty Hall problem. Since I have the best explanation than anyone else I might post it here. But the book is correct the probability of staying is 33%.
(What is so confusing about this Monty hall problem? People just cannot seem to solve it )
Shell 1, Shell 2, Shell 3
Each with a probability of 1/3 that the ball is under
Suppose you chose shell 1
If the ball is under shell 1 then either shell 2 or shell 3 can be lifted and no extra information has been given
If the ball is under shell 2 then shell 3 is lifted.
If the ball is under shell 3 then shell 2 is lifted
Three possibilities all with equal probability
You're not confused by the correct answer? Then what's the problem? Googling for "Monty Hall problem" will give you many explanations. Mathematical answers don't work in a democratic way, it's not the majority answer which is right, it's just the correct one - so opinions don't really matter
Finally someone who thinks like me. I hate it when people say it is 1/2 because they think it is a philosophical question (like in science) and you can choose sides. The same thing why the entire infinity thing makes me really angry, because there are nice formal definitions for infinity and people (the non-mathematical sub-human people) love to manipulate it until nothing makes sense.
Here are some of the many versions....
Ifinity minus infinity is zero because when you have infinite apples and you remove all of them you have left with none.
One divided by zero is infinite because when finding the number of times zero goes into 1 is infinite because adding zero keeps producing zero.
The log of a negative number is minus infinity because when you raise an exponent to a very large number you get zero.
And so on....
I am glad these guys are not mathemations.
Wikipedia gave me a better understanding of this problem (look under "Monty Hall Problem").
There is a 1/3 chance you pick the right shell to begin with, therefore there is a 2/3 chance it's in another shell.
The shell that is lifted up is merely a distraction, it changes nothing.