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I’m sure many of you are familiar with this problem before because it’s pretty famous. But just in case you haven’t here’s a great little video explaining the ’Monty Hall Problem’.
The vast majority of people first assume that switching choices after the first stage makes no difference. Simply because the choices left would suggest that you still have a 50/50 chance of choosing the prize. Hopefully that video explains why you would be much better to switch than stick with your original choice.
The best explanation I’ve seen is on the BBC web site by my favorite TV mathematician Marcus du Sautoy. You can catch the show on the BBC website at this address – http://www.bbc.co.uk/news/magazine-24045598 – here they actually run a small experiment to demonstrate the logic behind this problem.
Soem people may have problems watch the BBC video from outside the UK as it’s linked to a BBC show about Mathematics. Apparently there are some licensing restrictions and stuff which prevent you accessing the video content – try this site which can with issues like how you can watch British TV even when in the USA or outside the UK – http://www.onlineanonymity.org/uk-tv/how-to-watch-uk-tv-in-usa/.
It’s a great little problem though for anyone interested in probability and for anyone fooled into the 50/50 assumption don’t worry – many famous mathematicians made the same mistake first. It’s so counter intuitive to our understanding of probability theory on first sight it’s easy to see why it’s so confusing.