I recently came across this problem and thought that the answer was fairly obvious. I took the problem to an actuary who would of course know about these things and he too thought the answer was obvious. The problem relates to an American gameshow from the '70s.
You're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?"
What should you do?
The majority of people 'know' what the answer is, and yet the majority of people got it wrong. When this first appeared in Sunday Parade many readers, including some rather serious mathematicians argued that the solution was incorrect. This argument has also raged in a number of other academic circles.
The reason to raise this is that sometimes the obvious is never obvious. Sometimes it takes a lateral perspective to get to the real underlying issue. Our view is that creating compelling solutions is where quality analysis meets constructive innovation. This is the source of great strategy. A great idea, no matter how obvious is not always the right idea.
By the way, if you are still wondering, if you are on the gameshow and offered this opportunity then you should always change the door you chose. If you stick your chances of winning are remain one in three and by changing they increase to two in three.