Probability explained | Independent and dependent events | Probability and Statistics | Khan Academy

What I want to do in this video is To give you at least a very basic overview of the possibilities Odds are, a word you may have heard a lot. , That you may know about it in a simple way. Hopefully this will give you some deep understanding of it. So let's say I have a regular coin here. When I'm talking about a regular coin, I mean it has an equal chance that Down on one side.

That is, the probability of the appearance of both sides is equal Because its weight is equal on both sides When I flip it in the air Neither side is more likely to appear than the other The probability of each appearing equal We have this side of the coin We call it "the face" I'll try to draw George Washington I'll assume that's a quarter And the other side we call "back." This face And the other part here is the back So if I ask you What is the probability? I'm going to throw a coin I want to know What is the probability of the appearance of a face And I'll write it like this The possibility of a face Depending on this question You may have understood what is meant by probability It is a specific method To understand a specific incident This incident is basically a random one We do not know which side or back of the coin will appear when we toss it But we start by describing the chances of emergence The face or the back of the coin And we'll talk about several ways to explain that One of the ways And this is how They explain "possibilities" in textbooks She asks that How many possibilities can occur in this experiment OK How many possibilities can occur in this experiment How many possibilities can occur in this experiment I want the numbers that achieve the required event here Well, the number of possibilities Which fulfills the conditions Which fulfills the conditions In this incident or "experience", the incident of coin tossing and the appearance of the obverse of the coin How many possibilities in general We only have two possibilities Assuming that the currency will not fall on one of its corners It will fall directly It will fall directly Well we only have two possibilities here The two possibilities are equal You will get either on the face or the back of the coin And how many possibilities Which fulfills the conditions Here we have one condition, which is the appearance of the face of the coin It will be 1/2 This is a method for calculating the probability of showing the face of a coin when tossed It equals 1/2 It equals half If you want to write it as a percentage We all know that half is equal to 50%.

Now I will explain it in another way It is a method of visualizing possibilities Which will give you exactly the same result If I'm going to have an experiment Toss the coin When you imagine this experience happening I know it's not an experiment That I'm used to You might think only experiences Chemical or physical experiments. But an experiment is an accident that happens randomly Well, one of the ways to calculate probability If you do this experiment many times If you did it a thousand times or a million times Or a billion times or a trillion times The more we do the experiment, the better What is the percentage that achieves the result I want How often does the face appear? An other way 50% chance of getting the face of the coin It is when I do this experiment many times Even if I do the experiment forever Or even an infinite number of times What is the proportion of the appearance of the face The percentage will be 50%.

And you can do the experiment yourself, throw the coin You will definitely be heard I advise you to do the experiment If I took a hundred or two hundred currencies Put them in a large box, and move the box As if you are experimenting with tossing a coin with a large number of coins Then count the times that the face of the coin appeared And you will conclude that The more you do the experiment, the more The more you approach Get close to 50% But there may be cases Even if you do the experiment a million times There is a very small chance that the back of the coin will appear in all currencies in the box But the more the experiment was conducted You will notice that you are Get closer to that 50% of it will show the face of the coin Now let's apply the same idea And since we began to study the possibilities This is the basic idea of ​​probabilities And it is easy to visualize And it helps with that Conduct the experiment Many times And the percentage you get in those experiments She is the one who answers your question For example, in this case, what was required was the possibility of the appearance of the face of the coin Now let's take another example, which is a very common example When you are just starting to learn the possibilities He is throwing the dice This is the dice Of course, as you know We have several faces This is the first face, this is the second, and this is the third Now you know I'm going to suppose that There are six equal possibilities When you roll the dice The chances are that you will get one, two, three, or four Or five, or six equally If I ask you what is the possibility When making a dice test When the probability of getting any of the six sides is equal What is the probability of getting 1? Well, how many possible possibilities? I have 6 possible possibilities How many possibilities that fulfill the conditions? Only one of them fulfills the condition Here I have 1/6 probability of getting 1 What is the probability of getting 1 or 6? one more time There are 6 possible possibilities There are two possibilities that fulfill the condition You may get 1 or you may get 6 I have two possibilities that fulfill the condition I have two possibilities that fulfill the condition The probability of getting 1 or 6 = 1/3 Now what is the possibility ..

The question may be silly, but … To understand more, I will ask What is the probability of getting 2 and 3? Here, I'll roll the dice only once Well, every time I roll the dice I get either 2 or 3 only Here, I don't mean to roll the dice twice and get 2 and 3 In this case I have 6 possibilities None of these possibilities 2 and 3 together In one experiment Cannot get 2 and 3 in the same experiment Cannot have 2 and 3 at the same time Impossible to happen in the same experiment So the probability of this is zero In the case of a regular roll of dice, it cannot be obtained On 2 and 3 together I don't want you to think about it too much Because it is impossible to happen So cross out this phrase Now what is the probability of getting an even number? Once my brother, we have 6 equal odds When I roll the dice Which of these possibilities fulfill the conditions? Provided that the number is even Well, 2 is even, 4 is even, and 6 is even So 3 of the possibilities fulfill the condition It is that the number is even Well here 1/2 if you roll the dice I have a probability of 1/2 to get an even number

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