Hedge Fund Brainteasers: Two Buckets and 100 Balls

You have 100 balls, 2 buckets, 50 balls are black, 50 balls are white.  How do you set up the 2 buckets of balls to give yourself the greatest probability that you will choose a black ball?

How this makes you a great investment banker or hedge fund trader, I don’t know!  This is the kind of question they may ask to get an idea of how you think on the spot when the pressure was on.

Here is how to do it.  You take one black ball and put it into one bucket.

That gives you a 100% probability on that side.  On the other side, you put all the other balls.  So, one bucket has 99 balls, of which 49 are black and 50 are white.  The other bucket has one black ball in the bucket.  How does this work?

Obviously, one bucket has a 100% probability and the other bucket has slightly less than 50% probability.  Let’s round it out and say it is 50% (it’s probably closer to 49.5%).  So, on one side you have 100% on the other side you have 50%.  Thus, your probability is just less than 75%.  Those are the highest thoughts that you can get.  That, of course, is assuming that someone is a completely random way of choosing a ball.  It’s not like they are going to be staring at the buckets; they’re going to be blindfolded when they do it.

That’s the way to answer this question.  You put one black ball in one bucket, 99 balls in the other and you have just under 75% probability.

Ⓒ The Big Game Hunter, Inc., Asheville, NC 2020

ABOUT JEFF ALTMAN, THE BIG GAME HUNTER

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