Rule of Product
This is the only concept I go over in this post. The second half is my struggle with probability as a subject.
When flipping a coin, the probability of me flipping a head is 50%, or 1/2
Every… single… time we flip a coin, it is a completely independent event.
A coin never thinks, “Hmmm, I’ve been landing on tails a lot, so I’ll make sure to land on heads next time”.
So us predicting the next flip is a single event.
Now if we want to predict multiple independent events, we use the rule of product.
So if my chance of flipping heads on the first flip is 1/2 (I hate fractions with a passion, but I admit they’re easier for this), the chance of us flipping two heads in a row would be 1/4.
To take it further, our chance of flipping three heads in a row would be 1/8
So for every independent event you add to the trial, you double your chances of it happening consecutively.
What’s the Chance I Wouldn’t Care About Chance?
Alright, I’ve done 3 different ‘intro to probability’ courses and I’m still lost on what exactly this is used for.
Moreso, I don’t see how precise probability applies to the real world outside of gambling and machine learning.
No really, for everyday things like weather, we only care about more or less likely (over or under 50%). Past that, nobody goes about doing a bunch of calculations just to find out if something will happen or not.
In what possible scenario is telling me “You have a 72.841% chance of this working” any more helpful than simply saying “You are more likely to succeed at this”?
Or like in those action/sci-fi movies where the nerd scientist will say “The odds of this working are 88,256,373 to 1!!!” while all the other characters ignore him and still succeed at the challenge they were facing. What was the point in doing all that calculating instead of just saying that this is closer to possible or impossible?
This is only increasing my frustration because I have to learn this for machine learning, yet I don’t know where to start learning probability without jumping straight into the complex. Even the two statistics college classes I took barely scratched the surface of probability. Like I said, once you get past coin flips and dice rolls, you go straight into Greek letters and tangled equations.
So, I now have no other choice but to learn this through casino games. This is the simplest field I can start with that doesn’t require as much calculating as other fields like medicine or insurance.
So in my next post, I will be starting with two basic casino games and deconstructing their probabilities. They may be different once I actually post it, but as of now, I’m thinking blackjack and dice will be my first victims, given their simplicity.
Grant Abraham 