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Microsoft Program Manager Interview Question

I interviewed in Redmond, WA and was asked:
"You are on a game show. There are three doors, behind one of which is a prize and the other two is a chunk of coal, and the host knows which door holds the prize. You choose door #1. Before it is opened, the host opens door #3 and reveals a lump of coal. You have the choice to stick with the door you chose originally or switch to door #2. What do you do?"
Tags: brain teaser, puzzle
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Answers & Comments

7
of 12
votes
Switch doors. When you chose door #1, there was a 66% chance that the prize was not behind that door. When the host revealed the coal, there was still a 66% chance the prize was not behind the door you chose. Thus, you have double the odds of getting the prize by switching to door #2. The key to this puzzle is that the host knew which door has the prize.
- Interview Candidate on Jan 27, 2011 Flag Response
3
of 13
votes
That is not true. The probability went from 1/3 to 1/2 once the number of doors reduced to 2. However, statistically speaking, your chances of finding the treasure are now even. So it should not matter which door you pick.
- Murthy on Jun 23, 2011 Flag Response
3
of 4
votes
Interview candidate is right. You got 1/3 chance that prize is behind door #1 and you lose if you switch. And you got 2/3 chance that prize is behind either door #2 or #3. Since the host will always eliminate the wrong one. 2/3 chance will be allocated on the left one.
- Anonymous on Jun 27, 2011 Flag Response
1
of 4
votes
Everyone is wrong. You stay with your first pick, the odds becoming slanted greatly against the other door.
- scooter58 on Jul 11, 2011 Flag Response
2
of 3
votes
Interview Candidate and Anonymous are right. This is also known as the Monte Hall problem
- Tony on Jul 12, 2011 Flag Response
4
of 4
votes
Your choice splits the doors in two sets. Set A contains the door you selected, and the probability that is a prize behind this door is 1/3. The set B contains all remaining doors, and the probability that the winning door is somewhere in there is 2/3. By removing one door, which all have the success probability of zero because there's coal behind them, from set B, only one door remains in B, but the overall probability for success in set B is still 2/3. Therefore you must switch.
- Manish on Jul 25, 2011 Flag Response
0
of 0
votes
I can't believe that some of the answers up here actually state that you should switch.
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Before the host showed you that door#3 was hiding coal, your chances to pick the right door where 1/3.
Now that you know that coal is behind door#3, you only know that 1 of the 2 remaining doors leads to coal while the other leads to the prize.
While your probability of making the right choice has increased from 1/3 to 1/2, this probability still applies to both of the doors. You can't differentiate them.

Seriously.
- Tarik on Oct 18, 2013 Flag Response
0
of 0
votes
Tarik,

You are correct that the right choice has increased from 1/3 to 1/2, but you have to account for variable change in this instance.

Think of the same problem, but with different numbers. 100 doors, same conditions. You pick 1 door, with a 1/100 chance of being correct. The game show opens 98 doors with coal (because he knows where the prize is). He now offers you the chance to keep your door or switch to the last remaining door. In this

Because of variable change you will always be better off switching doors.
- Averee on Jun 18, 2014 Flag Response
0
of 0
votes
Scratch that, the right choice hadn't increased from 1/3 to 1/2. It's late and I have no idea why I typed that.
- Averee on Jun 18, 2014 Flag Response

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