How To Solve Amazon's Red Ball Lottery Interview Puzzle

Asked at Amazon

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[Bodyknock]

This problem is interesting because, while it's easy to guess the solution is putting one red ball in one urn and the rest in the other, the tricky part is actually mathematically proving that the solution is the optimal solution.

[William_Li]

hey I finally figured one of his riddles out!

[itskelvinn]

Pretty much common sense once you realize you can put one ball in an urn.

[JohnLeePettimoreIII]

This one I "kinda got". I went with my gut instinct to put one red in A and all the rest in B. My reasoning was, B would give just slightly less than 50%, but the 100% of A would "average it out" to about 75%. So while I was mostly right, it appears I got it right for the wrong reasoning.

[giladzxc]

couldnt concentrate after you said blue balls

[Puzzlefilia]

1 red ball in one urn, and all the other 199 balls in the other urn, and you have a winning probability of nearly 75% without great calculus. Great puzzle!!!

[ViktorLox]

Figured it out before he even asked what the goal was

[HagenvonEitzen]

Instead of using derivatives at 03:45, just observing r/(2r+1)= 1/2 -1/(4r+2) might be simpler

[Frgit]

it would be cool if you could lower the music volume

[diego]

Nice explanation! Have you ever considered putting out an ipython notebook or perhaps d3.js explanation as well? That way people can interactively explore solutions and how they vary with parameters.

[acediamond]

I believe, after a little thought, that the answer is:Put 1 red ball in one urn.  Put all of the remaining 199 balls in the other urn.You now have win probability of 1/2 * 1 + 1/2 * 99/199 = 199/398 + 99/398 = 298/398 = ~0.749, or ~74.9%.

[BobCliffe]

I personally liked the music, and hadn't particularly noticed it until reading the comments where everyone else was talking about it.

[alejopijuan]

Finally! First puzzle I've figured out.

[vicr]

I do like the music. Keep it, but make it just a little bit quieter. :)

[TheClash]

I like your videos. Personally, I find the music distracting.

[xnick_uy]

The problem was easy, but I found the proof of optimality quite elegant.

[FourthDerivative]

I like the music. It reminds me of the old educational VHS tapes we would watch in middle school.

[snowfloofcathug]

I figured it out in the wait for the explanation, easy, but still fun and challenging :)

[DJ-xonb]

You could also put all the red balls on top and the blue on bottom. Just grab the one on the top. They didn’t say it would be shaked

[christianfunintuscany]

Best strategy is to put just 1 red ball in an urn and the rest of the balls in the other one. This way we maximize the probability to pick a red ball which is 74, 8%. There are several ways to proove that this is the max probability for this event: we can distinguish classes of possible distributions for the solutions by the way balls are organized in the urns. For each class we can calculate max probability, then we can compare the max probability of each class. Another way to proove that’s the max probability is to show that any change in the balls distribution decreases the probability. I think this is the easiest way.