Well, there’s only one, the condition of heads. So the probability of this is actually 0. If I flip it in the air, it’s not more likely to land on one side or the other. And of course, you have, you know, the different sides of the die. On one trial, you cannot get a 2 and a 3 in the same experiment.
Now, let’s just apply these same ideas. So number of equally– let me write equally– of equally likely possibilities. I could roll a 1 or I could roll a 6. And what I want to do– and we know, of course, that there are– and I’m assuming this is a fair die. Well, 2 is even, 4 is even, and 6 is even.
Well, only one of them meets my condition, that right there. You could either get heads, or you could get tails.
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Well, what are the number of equally likely possibilities? And so you have one side of this coin. And mastsring always some chance– even if you flipped a coin a million times, there’s some super-duper small chance that you would get all tails. Getting a 2 and a 3 are mutually exclusive events.
And this is the idea of rolling a die. Now, let’s do another very typical example when you first learn probability. Now, what is the probability– and this might seem a little silly to even ask this question, but I’ll ask it just to make it clear. And while we’re starting with probability, at least kind of the basic, this is probably an easier thing to conceptualize. Well, I have six equally likely possibilities. Theoretical and experimental probability: Intro to theoretical probability.
So if I were to ask you, what is the probability given that I’m rolling a fair die– so the experiment is rolling this fair die, what is the probability of getting a 1? So the number of possibilities that meet my constraint, that meet my conditions.
In this case, it was heads. Well, once again, there are six equally likely possibilities for what I can get.
Intro to theoretical probability
And of the number of equally possibilities, I care about the number that contain my event right here. So that is heads. What is the probability of rolling a 1 or a 6? What percentage of those would give me heads?
Interpreting results of simulations. Now, let’s just apply these same ideas. So the probability of this is actually 0.
I know this isn’t the kind of experiment that you’re used to.
I could roll a 1 or I could roll a 6. I encourage you to do it. So you can maybe view it as the sides are equal, their weight is the same on either side.
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So one way to think about probability is if I were to do this experiment, an experiment many, many, many times– if I were to do it 1, times or chaptet million times or a billion times or a trillion times– and the more the better– what percentage of those would give me what I care about?
We’re assuming that the coin can’t land on its corner and just stand straight up. Random number list to run experiment. The other side right over there is tails.