On Tuesday I proposed a question of probability. The correct answer to the problem is to swap, since it does net out a better possible outcome by a marginal, but measurable degree. As Mark said in a comment, this is a derivative of the Monty Hall problem.
This question is used by interviewers for jobs on trading desks, too.
The Monty Hall problem is named after the man who hosted the TV show “Let’s Make a Deal.” At the end of the show, the contestant was asked to pick from one of three doors. Behind one door is a car, behind the others are two goats.
After the contestant makes their choice, the door is opened to one of two doors that were not selected. The goat appears. Now the contestant has to make a choice, he or she can swap their door for the remaining unopened door or keep the door originally picked. The contestant should choose to switch, as it would improve their odds dramatically. In fact, the door originally chosen has a 1/3 probability of winning, whereas the remaining unopened door has a 2/3 probability.
Wikipedia explains this best with this drawing:
According to the Wikipedia page from which I’m stealing the majority of the content here, the magazine Parade ran an article showcasing the mathematics behind the decision. More than 10,000 people wrote in to disagree, thinking that it didn’t matter. It does. Interestingly, more than 1,000 of the 10,000 people had PhDs.
In just one week, we’ve already beat MBAs at retirement planning and PhDs at basic algebra. Next week, we’ll talk about methods to walk on water.