Testing out the Monty Hall problem

Alan Davies and Oxford Mathematics Professor Marcus Du Sautoy test out the Monty Hall problem.

I'm posting this with regards to the comment thread of the following video:

http://www.youtube.com/watch?v=mhlc7p...

Even with a clear explanation of the problem, many people still can't grasp its logic. Hopefully, after watching Alan and Professor Du Sautoy's demonstration, they get a better understanding of it.

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  Education

[Michael Brown]

BBC Horizon: Alan and Marcus Go Forth and Multiply

[GroovyDancin123]

This is due to the fact that you have a 2/3 chance ( ~ 66% ) chance of getting a goat first try: there are three choices, two goats, yet there is only one car which has a probability of 1/3 ( ~ 33% ) Chances are, you will pick a GOAT first try because of the higher chance. Since the host reveals one goat ( which means you cannot switch to another goat if you picked it first try ) you will now have a 2/3 chance ( ~ 66% ) of getting the car! Very confusing, but quite simple when you get down to it

[NzPwMr]

Yes correct, so in this special case scenario, 33/100 times you will win a car if you choose to stay, and 33/100 times you will win a car if you choose to swap.

Stay scenario; 1/3 chance to pick the car and win

Swap scenario: 2/3 chance to pick the goat, 1/2 chance host will pick car and you lose , 1/2 chance host will pick goat & you swap and win; this diminishes your 2/3 chance to 1/3 because 2/3 x 1/2 = 1/3

[HumptyDumptyOakland]

You didn't read what I wrote.If the host DOESN'T know where the prize is and opens a goat door by chance then it's 50/50 between your door and the door the host didn't open

[thewolf465]

People have such a hard time understanding this concept.

[thewolf465]

You are incorrect.  Your original choice never increases above 1/3. The host showing you another door does not increase the chances your choice was correct.

[HumptyDumptyOakland]

That's incorrect. If the host doesn't know where the car is and opens a goat door by chance, then the chance you picked the car in he 1st place increases to 50% - so no benefit in switching.

[RajaTheFish]

it would still be in your favor to switch. If the host opens the car door, you lose no matter what according to your rules. If the host opens a goat door, its just like the original circumstance giving you a 2/3rd chance if you switch to win

[HumptyDumptyOakland]

I was assuming you can't switch to the door the host has opened, in which case there's no benefit in switching if the host happens to open a goat door (if he opens the car door you lose automatically)

[RajaTheFish]

in that case it would still give him an advantage to switch, because the host either shows him the car (which he would obviously switch to) or a goat, and if the host showed a goat, it would be the same probability as that which is shown in the video. The host not knowing which door holds what would only increase the odds of winning the car since he could open the car door.

[HumptyDumptyOakland]

If the host doesn't know where the prize is then there's no benefit in switching, you're just as likely to have picked the prize in the 1st place