A Microsoft Interview Question (aka basic Bayes' Theorem)

[Kaz The Original]

Ok. First off you're a freak : )

I do not understand Bayes Theorem and will give my laymans approach to this problem. You are in two situations and have the following piece of knowledge : The bullets are adjacent.

There is a 2 in 6 chance you will spin to bullet. 1/3rd of the time. The question is, does your friend having fired a shot increase, decrease or change this chance?

You now have 2 in 5 chance of shooting a bullet. This is obviously correct because if you fire 3 more times and get click you would then have a 2 in 2 chance.

The only information you gain from the bullets being adjacent is that their is not a bullet in both the next chamber and the chamber right before the one you just shot.

Spin again.

[tylerdurden]

I've asked this question to a lot of otherwise intelligent people, and almost every one of them got it wrong. The few that got it right were obviously guessing, except for one guy.

None of them (except the one guy) actually attempted to reason it out.

The education system (in the US, at least) emphasises rote memorization and discourages visualization and "working it out". When confronted with a question to which the student hasn't memorized the answer, guessing is the only remaining path.

Ever wonder why Asian kids are so good at doing arithmetic quickly in their heads? Nobody ever told them it was bad to use their fingers when counting. Using any means possible to visualize a problem is a much better skill than simply memorizing 7+8.

I had a professor for Differential Equations II that was from Japan and could do aritmetic very quickly. Now there are some people who can do simple arithmetic involving large numbers in their head, but don't understand how they do it, but I've met several of those people and this professor didn't seem like one of them (he was fast, but not instantaneous like the people that had the inherent ability). I asked him how he did it and he told me, "I just picture an abacus in my head."

The one guy who did get it right just drew the cylinder out on a whiteboard and had the answer in about 30 seconds.

[Paul2432]

[ QUOTE ]
From the rec.puzzles archive: "Four people need to get across a bridge that can only support two at a time. It is night and one of the two must carry a flashlight. There is only one flashlight. How can they get across in 17 minutes if their crossings speeds are 1, 2, 5 and 10 minutes?"

[/ QUOTE ]

The wiseass (and technically correct) answer to this question is that crossing the bridge is impossible. If the bridge can only hold two people, the added weight of the flashlight will collapse the bridge.

Paul

[Ed Miller]

Did you take off points, if the applicant pulled out a pen & paper? That's how i solved the problem & would have taken the same approach in an interview.

Use of pen and paper is encouraged. [img]/images/graemlins/smile.gif[/img]

HE, 10 players, a loose game, initial betting round. The 1st x players fold, say 4. It's now my turn to bet. Does the fact the 1st 4 folded mean that the remaining 5 are likely to have better cards than they would if a new deck was shuffled and these 5 were dealt another set of hole cards?

What you're talking about has a name... it's called "bunching." You can search for that word and find more discussion of this idea. Some authors think this is a significant effect, but I think they are wrong.

Dan Kimberg did some simulations about it.. he wrote it up in a Card Player article.

My feeling (and I know it's Mason's as well) is that the remaining players are ever so slightly more likely to have better hands, but that the effect isn't nearly large enough to incorporate it correctly into your strategy. (That is, any adjustment you consciously make is almost certainly going to be an overadjustment.)

[ddubois]

So why are manhiole covers round?

The "Microsofty"-question I like to ask in interviews is: "You are in a small pond, in a boat, with a cannonball. You take the cannonball and plop it into the water. Does the water level (once it has calmed) on the shore go up, go down, or stay the same?" It always depresses me how few people get this question correct, and don't really try to work it out.

One of the coolest interview questions I've been asked was: "You wish to use two cubes to represent a day calendar. In other words, you want to be able to arrange the cubes such that the tops show anything from [0] [1] to [3] [1], inclusive. Can you do this, and if so, what numerals do you enscribe onto each face of each cube?" The reason I liked this so much is that there is the initial logical aspect of the solution that gets you 90% of the way, which has to be worked out like most of these puzzles, and then to get the last 10% there is an additional hurdle that requires some out-of-the-box thinking.

[Jamper]

Thanks for the reply.

It's puts my mind more at ease now b/c I knew there had to be some effect, however small. The Bunching keyword led to several threads and a link to the Card Player article.

It was getting to the point where I was comptemplating running my own simulation [img]/images/graemlins/shocked.gif[/img]

-jamp

[buzzbait]

[ QUOTE ]

One of the coolest interview questions I've been asked was: "You wish to use two cubes to represent a day calendar. In other words, you want to be able to arrange the cubes such that the tops show anything from [0] [1] to [3] [1], inclusive. Can you do this, and if so, what numerals do you enscribe onto each face of each cube?" The reason I liked this so much is that there is the initial logical aspect of the solution that gets you 90% of the way, which has to be worked out like most of these puzzles, and then to get the last 10% there is an additional hurdle that requires some out-of-the-box thinking.

[/ QUOTE ]

For this I would set up one cube with faces of 0,1,2,3,4,5 and the other with 0,1,2,7,8,6 with this last face also used as 9, as 6 and 9 are never needed at the same time (In the day calendar that is, get your mind out of the gutter [img]/images/graemlins/wink.gif[/img] )

[Derek in NYC]

Part of the confusion by those who failed to get the right answer may come from a lack of familiarity with the way revolvers work. In a revolver, with each trigger pull, the cylinder holding the bullets rotates exactly 1/6 of the way, the hammer cocks, and releases on the cylnder that has just rotated into alignment with the barrel. If there is a bullet in that cylinder, the gun goes bang; if not, it goes click. On the next trigger pull, the same thing happens. After 6 trigger pulls, the hammer has cocked and fallen on every cylinder of the gun, and discharged all the bullets in all the cylinders.

A different problem. You and your friend wish to play Iraqi Roulette, a variation on Russian Roulette. A friend hands you a Glock pistol, inserts a fully loaded magazine into the gun, firmly seats the magazine, and cycles the slide. Who should go first? You or your friend?

[guller]

I think I would bet against the odds on this one and spin. For all the marbles (my life) I would want to get some of my own luck involved on this decision.

If the cylinder was weighted by the 2 bullets wouldn't they tend to settle on the bottom away from the firing pin more often than not?

[dblgutshot]

[ QUOTE ]


A different problem. You and your friend wish to play Iraqi Roulette, a variation on Russian Roulette. A friend hands you a Glock pistol, inserts a fully loaded magazine into the gun, firmly seats the magazine, and cycles the slide. Who should go first? You or your friend?

[/ QUOTE ]


I have no knowledge of handguns, but is it more likely that a bullet or gun would get jammed on the first shot rather than the second?

The obvious answer is to go second, so your friend blows his brains out and you can leave!