What is probability?

Tivadar Danka small portrait Tivadar Danka
Relative frequency of occurrences

Understanding math will make you a better engineer.

So, I am writing the best and most comprehensive book about it.

You are (probably) wrong about probability.

I'll show you. How many heads you'll get if you toss a fair coin 1010 times?

If you answered 55, here is why you are wrong.

(Below is the 100 HUF coin, if you were wondering.)

Probability of a coin toss outcome

You might as well try it if you have a coin in front of you.

All we can say with 100%100 \% certainty is that the number of heads will be between zero and ten.

However, that's not all to it.

Number of heads after ten coin tosses

For instance, the probability of landing 88 heads and 22 tails is approximately 4.39%4.39 \% .

What does then the 1/21/2 probability of heads mean?

Probability of 8 heads and 2 tails

Let's keep tossing the coin. Even though the number of heads and tails varies, it will fluctuate around 1/21/2, that is, the probability of heads.

This is what probability represents.

Relative frequency of heads

In general, the relative frequency converges to the probability.

(The relative frequency is the ratio of occurrences of a given event and the number of experiments.)

This is the frequentist interpretation of probability.

Relative frequency of occurrences

The frequentist interpretation is only one side of the coin, so to speak. If you are curious about the full picture, check out my recent post about the frequentist and Bayesian interpretations!

Having a deep understanding of math will make you a better engineer.

I want to help you with this, so I am writing a comprehensive book that takes you from high school math to the advanced stuff.
Join me on this journey and let's do this together!