/sci/ - Science & Math

imagine this....

>you're on a cruise paid for by Karl's Jr.
>the host picks a door between left and right.
>the host knows where the car is and will therefore always pick the car door for himself.
>the player, you, only know that 3 doors exist.
>you are not inside the normal universe, and so you cannot see what the host sees or what is behind the door the host picked to validate whether they have actually chosen a car or i have lied to you.
>behind one of the doors is a red ball, behind the others, a goat, and a car exists so for the sake of posterity behind the 3rd door is a brand new door that has never been used and only has some dings and scratches.
>what is the mathematical probability of choosing a door?