I’m struggling in high school with this stuff.
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I will start by answering **”what is randomness?”**.
When you roll a die or flip a coin, the result is random, right?
Well… technically if you take the same die twice, roll it from the same position, give it the exact same speed, the exact same rotation, and have all the air molecules be at the exact same position, and have the dice be in the exact same position (up to a single atom) in your hand, and etc, then you would get the same result twice.
The only randomness here is that there are uncontrolled factors. You can’t replicate the exact same “rolling the die”, both because you don’t know all the informations about the exact position of the dice, and because it is humanly impossible to rearrange everything exactly the same.
Randomness is a mathematical tool that we use to understand better what we can’t control. And in the case of rolling a die, experience has showed that each face of the 6-sided die is obtained with a probability of 17%.
So, **what is probability science?**.
Like all science, it is decomposed in two steps: predicting and modelling.
1. When you’re doing prediction, you are give an hypothesis like “this is a fair coin with 50/50 chance of getting head or tail”, and you are tasked with computing the probability of an event, like “getting 4 heads in a row” (the answer is 7%).
2. When you’re doing modelling, you’re given a real situation with a bunch of statistics, like “we flipped this coin 153 times and obtains 82 heads and 71 tails”, and you’re tasked with finding an hypothesis like “this is a fair coin with a 50/50 chance of getting head or tail” that reasonably matches the reality.
In high school, I don’t think you will be doing the (2) very often. You’ll focus on (1), that is situations where other peoples before you already found reasonable hypothesis… or with totally artificial scenarios that have no basis in reality but give nice mathematical exercises.
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