This is a famous puzzle, called the “Monty Hall Problem”. Monty Hall was a host in the early episodes of the game show Let’s Make a Deal.
The common version of the the puzzle used three doors (instead of 3 boxes) and a car and two goats (instead of gold and garbage).
The problem was originally posed by Steve Selvin and became famous when it was quoted by Marilyn vos Savant in Parade magazine in 1990.
The answer: You increase the probability of winning the gold if you change your choice of the box to open. The probability of winning the gold is only 1/3 if you continue with your original choice and 2/3 if you change your choice.
Here is a brief explanation of why:
When you initially selected a box, you had a 1/3 probability of being right. The host knowingly opened a box with garbage in it, so that eliminated one of the wrong choices. You still have a 1/3 probability that you initially chose the right box; this means that the other unopened box has a 2/3 probability of containing the gold.
Amit Bhattacharjee, Satish K Mariyappagoudar, and Patrick OToole got it right.
Better explanations are provided on the wikipedia page here.
Or you can watch the youtube video.
If the video does not load, the link is http://www.youtube.com/watch?v=mhlc7peGlGg.
You can also search the internet for the keywords “Monty Hall Problem” – you will get lots of hits.
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Nothing Official About It! – The views presented above are in no manner reflective of the official views of any organization, community, group, institute, country, government, or association. They may not even be the official views of the author of this post :-).