William Briggs explains the solution to the Monty Hall problem:
Many of you will already know the answer, but read on anyway because it turns out to be an excellent example to demonstrate fundamental ideas in probability.
Incidentally, I just did this yesterday to a group of surgical residents [this was in 2012]: you might be happy to know that none of them got the right answer. One even insisted—for a while—that I was wrong.
That last line is so frequently a problem with academic types. They’re born with above average IQs and they’re used to being the quickest wit in the room. So when they’re presented with obvious reasons that they’re wrong they simply infer that their interlocutor is wrong or stupid. It’s one of the reasons I hate being around academics, they rarely discuss to discover the truth but only to air their opinions.
Anyway, go read the whole article. When I used to teach statistics and probability, my students always found their minds blown.