The Monty Hall Paradox:
Suppose you are the contestant in a game show and given the option to choose from 3 doors. Behind one there is a car and behind each of the other two a goat.
Now you pick a door, the game show host opens one of the two which you didn't pick and which has a gaot behind it. You are now given the option to switch your choice and pick the remaining third door.
Here comes the Paradox:
In any case there are one car and one goat remaining behind the 2 residual doors. Howerver if you switch, your probability of winning the car is 2/3 and not 1/2!
naw because its a whole seperate choice now, if you were to change your choice then the question has become choose 1 of 2 doors not 1 of 3.
your original chances were 1/3 but as soon as a door is opened and you get the choice to swap it becomes 1/2
Ah, the paradox works :D
No its not an independent choice because the initial state depends on your previous choice.
You have a 2/3 chance to choose a goat initially, the host is guaranteed to eliminate the other one, when you switch then you will win the car. You have a 1/3 chance to choose the car initially, if you switch then you will lose
so if you switch you have a total chance of winning of 1×2/3 + 0×1/3 = 2/3