In a game show youre presented with three doors behind one...

In a game show, you're presented with three doors. Behind one door is a car, and behind the others, goats. After you choose a door, the host, who knows what's behind each door, opens another door, revealing a goat. You're then given the choice to stick with your original pick or switch to the other unopened door. With perfect information, what's the best strategy?

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Transcript

00:01 Imagine that we are on a game show with three doors.

00:05 So we have three doors, behind one of them, there is a car, behind the other two, there are goats.

00:11 We pick a door.

00:13 Then the host, knowing what is behind each door, opens another door, which will always have a goat.

00:20 Then you have a choice.

00:21 Do you pick with your original, do you stick with your original door or do you switch? what should you do? so this is a very famous problem called the monty hall problem.

00:34 And the answer is you should always switch.

00:40 Let's have a look at why.

00:42 Imagine you always pick door number.

00:46 There are three equally likely outcomes.

00:49 The car is behind door one, so we'll have one, behind door two, behind door three.

00:57 So you have a three here.

01:00 Let's say it's behind door three.

01:02 So the car is here.

01:03 You've picked the wrong door.

01:05 Then the host will reveal door two.

01:09 They have two.

01:10 Because there's only two, you've picked one of them, the other one is going to have a goat.