Probability, Ratio, and the Law of Large Numbers

Probability and Ratio

You probably know about probability and ratio. Suppose I put 70 of black balls and 30 of white balls in an urn. General statements would be

• The Ratio of black balls (when comparing to all the balls in the urn) is 7:10
• If I draw a ball from the urn, the Probability that I would draw a black ball would be 7 in 10

Are They Different?

Ratio and Probability look very similar. For the above example, both the ratio and the probability is 7 in 10. But, in fact, they differs:

• Ratio is an act in the past. It is deterministic and measurable. You put 70 black balls in an urn. That's make the ratio 7 in 10. 
• Probability is an act in the future. It is probabilistic and uncertain. The chance to draw a black ball is 7 in 10. But it doesn't mean that, if you draw 10 balls, 7 of them would be black.

This definition discrepancy is filled up by what mathematicians known as the Law of Large Number.

The Law of Large Number

"It is always possible to have a finite number of observations such that the observed probability matches closely with the underlying ratio."

The Law of Large Number was stated without proof by Gerolamo Cardano in the 15th century, and was formally proved by Jacob Bernoulli in the 17th century. It is therefore also known as the "Bernoulli's Theorem" or a "Golden Theorem".

Loosely speaking, the law of large number say that the probability and the ratio would be the same if you carry out a sufficient large number of experiments.

Does It Have Implication in Real Life?

Yes. Here is one of them.

Suppose you are good at something. But you keep failing due to the randomness (i.e., bad luck). Then you should double (or triple) your effort (number of trials). Your effort (i.e., trial) will wipe out the bad luck (i.e., randomness), and people will see your true performance (i.e., ratio).


Source: The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow, Chapter 5 [Read the Book Review] [Read the Previous Part] [Read the Next Part].

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Book or Audiobooks?

Personally, I prefer audiobooks. It's fun, and I can listen when I'm doing something else. It also makes other activities (e.g., jogging) a lot more fun. For more detail about audiobooks, please read [this post].

There is one more reason that may encourage you to go for the audiobook version. You can get it now for FREE. Audible offers you a free trial for 14 days. Even if you get the book and cancel the subscription right away (so that you don't have to pay), you can keep the book. And, don't worry if you lost the audiobook file. Just log into audible.com. You can keep downloading the over and over again.


About the summary: It takes time to finish up a book. And, when you do, sometimes, you want to review what you learn from the book. If you do not make notes as you read, you might have to go through the book once again. This can be time-consuming when you are dealing with a book. But you can still flip through the book and locate what you are looking for

However, when the material is an audiobook, it is extremely hard to locate a specific part of content. Most likely you will have to listen to the entire audiobook once again.

This book summary will help solve the pain of having to go through the book all over again.

I am leaving out the details of the books. Most books have interesting examples and case studies, not included here. Reading the original book would be much more entertaining and enlightening. If you like the summary, you may want to get the original from the source below.