## xyz Interview Question

Software Developers**Country:**United States

I think the answer is indecisive becoz, they are anyways opening the door having one of the donkeys.So even though I chose a the door behind which there is a mercedes in the first chance or the door having the second donkey in the first hand I will always be in dilemma to switch or lock with my second choice..

Corrections/Suggestions to my answer are welcome..

While 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.

- Greenskid July 31, 2015However 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)