Theoretical and experimental probability: So there’s two possibilities here, two equally likely possibilities. And so if I were to ask you, what is the probability– I’m going to flip a coin. And I don’t want to confuse you with that, because it’s kind of abstract and impossible. So the probability of this is actually 0.
So the number of possibilities that meet my constraint, that meet my conditions. We don’t know whether it’s heads or tails, but we can start to describe the chances of it being heads or tails. On one trial, you cannot get a 2 and a 3 in the same experiment. So once again, you have six equally likely possibilities when I roll that die. So in this situation, there’s six possibilities, but none of these possibilities are 2 and a 3.
Well, once again, there are six equally likely possibilities for what I can get. So one way to think about it, and this is the way that probability tends to be introduced in textbooks, is you say, well, look, how many different, equally likely possibilities are there?
I’ll assume it’s a quarter of some kind. Now, another way to think about or conceptualize probability that will give you this exact same answer is to say, well, if I were to run the experiment of flipping a coin– so this flip, you view this as an experiment. If I flip it in the air, it’s not more likely to land on one side or the other.
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And this is the idea of rolling a die. I could roll a 1 or I could roll a 6. You can flip a coin. We’re assuming that the coin can’t land on its corner and just stand straight up. Chaprer they’re all equally likely.
And there’s 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. Try to draw George Washington. Well, there’s only two possibilities. I’m not talking about taking two rolls of this die. So that’s the 1. And how many of those meet my conditions? I know this isn’t the kind of experiment that you’re used to. And the other side, of course, is the tails. And I could write that like this– the probability of getting heads.
We don’t know whether it’s heads or tails, but we can start to describe the chances of it being heads or tails.
Intro to theoretical probability
And I want to know what is the probability of getting heads. Random number list to run experiment.
ansqers Well, there’s only one, the condition of heads. Let’s say that I have a fair coin over here. Well, in any roll of the die, I can only get a 2 or a 3. And I don’t want to confuse you with that, because it’s kind of abstract and impossible. So let’s cross this out right over here.
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Probability, a word that you’ve probably heard a lot of, and you are probably a little bit familiar with it. So hoework 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 a million times or a billion times or a trillion times– and the more the better– what percentage of those would masetring me what I care about?
And of course, you have, you know, the different sides of the die. It’s asking for some type of way of getting your hands around an event that’s fundamentally random.
So that is heads. Now, let’s do another very typical example when you first learn probability.
So here’s my die right over here. So how many equally likely possibilities. And so if I were to ask you, masteering is the probability– I’m going to flip a coin.
So number of equally– let me write equally– of equally likely possibilities.