## Greenskid

BAN USERWhile one can apply simple statistics to get the answer it may not appear intuitive that it is better to always change from one's initial choice and choose the other door.

However if one considers a more extreme version of the same problem, then the answer is very intuitive... so imagine that there really was 1 million doors: your first choice would have 1 in a million chance of being correct. After you make your first choice, every door is opened except your original choice and one other door, such that the prize is either behind this door OR behind the door you originally chose. It should be clear now that your initial choice is still 1 in a million and that the other remaining door has (1 million - 1)/(1 million) chance of being the one you want.

So the chances of winning for the original question are:

- Keeping your original choice: 1/3

- Switching: 2/3 (3 - 1/3)

**CareerCup**is the world's biggest and best source for software engineering interview preparation. See all our resources.

Brute force searching for minimum:

- Greenskid August 01, 2015