# Probability by the Bucketful

# Probability by the Bucketful

Join the DZone community and get the full member experience.

Join For FreeHortonworks Sandbox for HDP and HDF is your chance to get started on learning, developing, testing and trying out new features. Each download comes preconfigured with interactive tutorials, sample data and developments from the Apache community.

Suppose you have a large number of buckets and an equal number of balls. You randomly pick a bucket to put each ball in one at a time. When you’re done, about how what proportion of buckets will be empty?

One line of reasoning says that since you have as many balls as buckets, each bucket gets one ball on average, so nearly all the buckets get a ball.

Another line of reasoning says that randomness is clumpier than you think. Some buckets will have several balls. Maybe *most* of the balls will end up buckets with more than one ball, and so nearly all the buckets will be empty.

Is either extreme correct or is the answer in the middle? Does the answer depend on the number *n* of buckets and balls? (If you look at the cases *n* = 1 and 2, obviously the answer depends on *n*. But *how much* does it depend on *n* if *n* is large?) Hint: There is a fairly simple solution.

What applications can you imagine for the result?

Hortonworks Community Connection (HCC) is an online collaboration destination for developers, DevOps, customers and partners to get answers to questions, collaborate on technical articles and share code examples from GitHub. Join the discussion.

Published at DZone with permission of John Cook , DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

## {{ parent.title || parent.header.title}}

## {{ parent.tldr }}

## {{ parent.linkDescription }}

{{ parent.urlSource.name }}