Statistics/Probability: How Do Computers Work With Chances and Lots of Numbers?

Statistical likelihood and probability is difficult for us to wrap our minds around, mostly because it deals with numerical values (which represent a certainty) applied to future possibilities (which represent an uncertainty).

Birthday Paradox

One example of unintuitive statistical projects is the birthday paradox:

  • What is the likelihood that X number of people will share the same birthday?

As much as it seems to be 1 in 365, the number pushes past 50% after 23 people.

The reason is relatively straightforward:

  1. Instead of looking at the number of birthdays, look at the number of individuals who have to pair with another.
  2. This means 23 x 22 / 2, which becomes 253.
  3. 253 possibilities is over half the number of days in a year (182.5).

Or, to look at it another way, Person 1 must compare their birthday with Person 2, 3, …, X, then Person 2 does the same with Person 3, 4, …, X, and so on.

This has far-reaching computer cryptographic implications with respect to hash versus block size.