Source: Various(Movies e.g. 21, Maths courses, books on basic probability)
Problem: Its Monty hall, also used in movie ‘21’,when Kevin spacey asks
Jim Sturgess in form of game show host problem.
You are on a game show and there are three doors. The presenter tells
you that behind one of doors there is a car and behind the other two are
goats. If you pick the car you win it. After you have picked a door the
presenter opens a different door with a goat behind it, he then gives you
the chance to change your choice to what door you open. What should you do?
Problem: Its Monty hall, also used in movie ‘21’,when Kevin spacey asks
Jim Sturgess in form of game show host problem.
You are on a game show and there are three doors. The presenter tells
you that behind one of doors there is a car and behind the other two are
goats. If you pick the car you win it. After you have picked a door the
presenter opens a different door with a goat behind it, he then gives you
the chance to change your choice to what door you open. What should you do?
Initially all the doors have the same probabilities i.e. 1/3,1/3 and 1/3
ReplyDeleteThe probability that your choice is correct is 1/3 and other way round is 2/3.
But you don’t know whether your choice is correct or not.
Now the game show host revealed the goat behind one of the door, so the 2/3 for the 2 doors becomes 2/3 probability for a single door, which is obviously greater then 1/3.
So if you change your choice your chance of winning goes upto 66.67 %