PROBABILIDADE \Prof. Gis/

Hi guys, I'm going to ask you something. On a wonderful sunny day, like that, when you wanted to go to the pool, did you even look up the weather forecast for the probability of rain for that day? Ah, so you already know what content Gis will explain today?

That's right, we're going to talk about probability. Another case where you can think about probability is also thinking like this, what is the chance of a person winning in the mega sena game, for example, or another classic example, what is the probability of a pregnant woman having a male child, see all these cases then involve probability. So if you have doubts and I want to learn more about this content, I invite you to attend this class.

Come on! Well then, welcome to our channel if before starting the explanation of what probability is and how it is calculated I want to ask you two things and you already know what Gis is going to ask for, so subscribe to my channel so if you have n't already written there, leave your thumbs up, ok. You've done that now let's go to class so it's not!

Oh! What is probability? In general, so a general explanation for you, probability is the chance of something happening, that's why I opened the class talking about the probability of rain.

It's the probability of something happening! Right and how do I calculate the probability? Look here, how do I calculate the probability?

The probability of an event that is something I am analyzing is not, so the probability is calculated like this: the number of favorable results divided by the number of possible results, ok, then when I calculate probability the result will be given in the form of an irreducible fraction or in some statements it will ask for this probability to be calculated as a percentage, just like in the weather forecast, the probability of rain is so many percent, ok, but I will teach you exactly how to do these accounts, but you were confused by all that is written here, weren't you? Ah, I knew it, so look at the summary I brought you using Gis's words, okay, you won't find that there in your book, in the activity, Gis is speaking in a simpler way for you to understand. So probability is what you want, okay, which would be the favorable results, what you're looking for divided by the total you have, so for example, I brought a dice here, okay, so if I said that, guys, if I throw this one given what is the probability of rolling 2?

So what am I wanting? I want 2 to come out, how many are these possibilities, one possibility because my die only has one side 2, right so what you want I want side two with the amount of do two is one, the total you have that is, here on the dice what is the total number of faces I have? There are six, so I would already be able to think of the probability of the fraction that would represent then what I gave as an example, it would then be the probability, it would be one because I have only one possibility of getting a two on my die since it has 6 faces and mine total here is six, because of the six faces I mentioned and, which one came out?

Five came up in my game, okay, so the probability would be a basket. This is an irreducible fraction, why is it an irreducible fraction? Because I can't find a number that is possible to divide the one and the six at the same time, okay, it's already an irreducible fraction ok.

So now let's do other examples. Come on people, so look at the examples I brought for us to apply this probability content. So when rolling a six-sided die, I already wrote that the die has 6 sides, because now we have those dice, the fancy things there, which have 8 sides, 12 sides, 20 faces, right?

It's those polyhedral shapes, right, but since here I only have the dice, the common six-sided die I'm going to use it, okay, so what's the probability that the face facing up is an even number? And now we, so I'm going to take a dice, oh another dice here, if I throw it upwards what will happen if I throw it upwards, will an even number come up? Oh!

Let's play, let's see what will fall? 2 even fell, what more, 1 fell is not even, it's odd, Oh if I play again, six falls is even, if you throw three again, it's odd, but I'll keep doing them all the attempts? Let's do the math so we can find out what this probability is, isn't it, so I need a number that's even and then you remember how the probability is?

So the reason is what you want, you want an even number to come out, look carefully, you have to pay attention to the statement, you want an even number to come out and then you will get the even numbers which are how many are the same here on the dice? Even number here on the dice is the number 2, number 4 or 6, that's not it, they are even numbers here on our dice ok, so here I have to get what I want, I have then three possibilities, three possibilities ok and now how am I going to set up the probability account then? Oh it's going to look like this, equal probability here in the numerator is going to be so what I want I want face even so I have three possibilities, so here it's going to be three, okay and, who stays even in the denominator is the total that I have, which is the total number of faces on my die, here on my regular die I have 6 faces, so the probability of this happening is 3 and 6 and if you look I can simplify this fraction so that I can make it an irreducible fraction, I I can take this here and divide it by three, okay, dividing this here by three I'm going to find 1 divided by 2, right, and if you have questions about how to do this simplification of fractions so that I can make it irreducible, I'll leave the indication of the class here so you can go back to watch and review these concepts, agreed?

So the probability, so I said that this measure was given in an irreducible fraction, isn't it, and, in some statements it is given in percentage, so the probability that an even number comes out when rolling my dice is one-half is the half right? Fifty percent, since my die has three even faces and three odd faces, ok. Look at the second example of rolling a six-sided die again, what chance do I have?

Here I wrote chance here I wrote probability it's the same thing ok guys? From the face up being a number greater than 2 now, so you should always pay attention to that restriction that I don't know it's giving me what I want now I want to roll the dice and the number has to be one greater than 2 , what are these possibilities of happening? Can you leave two?

Is it worth two? It doesn't matter, he said it's a number greater than 2, so it could be three or three satisfies the one I want, four, five or six, any one of them could come out that will satisfy what the statement is asking for. How many possibilities do I have here, one, two, three, four I have four possibilities, so what I'm looking for, possibilities, now let's set up our probability container, so probability is equal, remember the numerator is what I want I want , so that comes out a number greater than 2, so I have four possibilities, so here it will be 4, and what goes in the denominator is the total that I have.

How many faces are on my die? It has 6 faces, so it's four and six and then I can make it an irreducible fraction, doing what? Dividing by, in this case it's also two, dividing by two, four divided by two two is two, six divided by two is three, so it means that the probability of me rolling the die and that number coming up is greater than 2, that is, on these faces, either the number 3 or the number four or five or six, okay, I'm talking about it or, because any one of them can happen, it's two in three, okay, two thirds, but we say it's two in three, okay guys.

Let's do more examples, come on! People, look at the next examples that I brought, okay, now we're going to talk with the coins, play with the coins, which is also a very common example to find around, okay, to calculate the right probability, so look here when flipping a coin, so I'm going to pick up one of the two, then I'm going to toss it upwards, then it falls into my hand, it's there when I toss a coin what can happen? It could come up heads or it could come up tails, right?

I did the tails backwards, either heads or tails is fine, so what was announced? Asking you, have you read what is the probability of getting heads? And now people write the result in percentage, so what am I going to do?

Remember what the probability is like? What I want divided by the total I have, that's all, it's easy, what I want I want to come out heads how many heads do I have on a coin toss one head. So here the probability will be one face that I already have, one face in how many heads in total?

In two, and then the statement asks to write this result as a percentage, how do I transform this fraction in half into a percentage now? In case you don't remember how I turn a fraction into a percentage, I leave the indication of the class that we explained in detail how to do it, okay, and we know so here for me to calculate it, just divide the numerator by the denominator and one divided by two. you already know that it's half, isn't it people, half in percentage represents fifty percent, okay?

When in doubt, divide here one by two, it will be 0. 5. So 5 x 2 is 10 + 0.

5 because 0. 5 is 50%? Because now to get the percentage, I take this result and do it times one hundred, okay?

Oh, 0050 one decimal place one decimal place, fifty percent ok guys? So this coin thing is pretty classic to happen, okay? And look at the other one I brought here too, now we're going to use some little packets with a lot of colored paper.

Inside here there are several colored papers, there are only two colors, it's not very colorful today, in a bag it contains 10 papers so inside here I put 10 pieces of paper , okay, seven blue and three yellow, okay now, put the probability that I put your hand here with your eyes closed like this and raffle a little yellow paper. So what do I want? I want a yellow paper to come out.

Let's see how I was going to draw yellow? I'm not looking at production, I'm not looking, let's take this one here and this one is blue, not yellow, so, as I was asking, and then how am I going to calculate, so what is the probability of removing from this bag here a piece of paper that be yellow? Are you already thinking about it?

So I want yellow, yellow , there are three options for it to happen here, right? Because there are three yellow papers so the probability here is going to be equal to three because what do I want? I want the yellow paper to come out, there are three yellow papers, three in a total of ten, three tenths, three in ten, if the statement asks, if it's not asking, okay, if it asks to calculate this in percentage, that you would you?

You would divide three by ten ok, which would be zero comma and here would be three ok, so it would be 0. 3 and for me to get here in percentage or take the 0. 3 and multiply it by 100 = 0030 one decimal place one decimal place, then three out of ten is the same thing of 30%, so the chance of me picking up a piece of paper here that is yellow would be thirty percent ok, now let's do the last example of the day, let's go?

People, look at the other example I brought, so look at the roulette wheel numbered from 1 to 20. Where is the roulette wheel? It's here, so you 're going to look at the roulette wheel that Gis brought.

It is numbered from 1 to 20 so, for example, I'm going to take this roulette wheel just so we can play a little bit to see which number will fall, so you spin the roulette wheel, the first time the number 4 comes out, I'll spin it one more time time, then if I spin this roulette wheel again the number 8 comes out, once again, I like that little noise, oh listen and, now the number 7 comes out, you see then, different things happen here, every time I spin the wheel roulette drops a number, ok, and now, let's go back to the question: what is the question then? If Gis spins this roulette wheel, what is the chance of getting an odd number? People, the roulette wheel is numbered from 1 to 20, so there are the numbers 1, 2, 3, the numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20 is good!

What then will be the probability, the chance of rolling an odd number from 1 to 20? How many odd numbers do I have ? Can you think or do you want to, do you think it's better for us to write what all the possibilities are then?

Let's put here people 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20, it was a little tight here, look there, so I listed all the numbers, so that they are present there in our roulette wheel, okay? So leave the numbers here, what do I want to happen in this letter A? If I spin the roulette wheel and an odd number comes out, how many odd numbers do I have then?

I have 1 2 3 4 5 6 7 8 9 10 odd numbers, so the probability here is going to be, the probability, it's going to be so, what I want, I want an odd number and there's a 10 chance of that happening, so the probability is going to be 10, and what's the total number of numbers I have, twenty and then you remember how does the simplification? Because I always give the measure of probability using an irreducible fraction with which I can divide by two, by two, nothing is very good for you there who said, congratulations, I can now divide by 10, people, the two here are numbers divisible by 10 right, so I put here 10 by 10 is u1, 20 by 10 is 2 so the probability of an odd number happening there in the roulette draw is one in two that we saw since it's 50% okay? Now the next exercise, what is the probability then of getting a prime number now?

And then you already know that they are prime numbers? You don't remember prime numbers? So you're going to stop this video here, go back to the class that we're going to leave here, there's all the explanation of what prime numbers are, okay, I'll tell you here, so this sequence from 1 to 20 the prime numbers then are the 2 the 3 the 5 the 7 the 11 the thirteen the 17 and the 19 ok?

So I want a prime number to come out on this roulette wheel, what are the chances of this happening? One, two, three, four, five, six, seven and eight, so the probability of this happening will then be 8 out of 20, because eight possibilities of coming up with a prime number, which is what I want. And 20 is the total number of numbers I have on the roulette wheel .

And then I can do that simplification, I can simplify by four, okay, and then it will be 8 divided by 4 is two 2, twenty by four is 5, so the probability of this happening is and in five, the chance is good to happen is two out of five and then if the statement asked for a percentage what would you do? Divide two by five or divide, then do this in your notebook now 2 / 5 you will arrive at 0. 4, it arrived, check it, and then how do I transform it into a percentage?

I multiply the result by 100 so I'm going to multiply 04 by 100 which is 40% ok guys, do the count there and check with the Gis result here ok, look at the last one that comes out a multiple of 5 do you remember what are they multiple? So also pause this class and go back to that video that I'm going to leave here where I explained everything about multiples, they are the multiples of 5 here in this roulette wheel sequence, they are the number 5, let's do a pee at the bottom now, right, the five is the 10 the 15 and the 20, so the probability now will be what? What I want is a multiple of 5.

How many possibilities are there for this to happen? One, two, three, four, I have four possibilities out of a total of twenty numbers, okay, and then again I can simplify, I can see that you're going to have to stop there and watch the class on simplifying fractions, okay? , for you to become adept at this content.

I can simplify by four simplifying this here by 4 will give a fifth ok and then a fifth, a fifth will be what if I divide one by five, divide it and see if it gives the result of Gis, one divided by 5 is 0. 2 ok and 0. 2 which is 20%.

So the chance of something and in this case of turning the roulette wheel to get a prime number is forty percent and a forty percent chance of getting what I'm looking for, which is a prime number, okay, then in the letter c of getting a multiple of 5 is twenty percent is a twenty percent chance of coming up with what I'm wanting that would have a multiple of 5 okay and here in the first one it's a 50 percent, fifty percent chance of coming up with an odd number because I want the odd number to come out ok so, every time you solve probability questions you should always pay attention to the statement what he is asking you want actually I statement he is wanting it not so be very aware of the I don't want to open up okay , you do all the possibilities and always see who is the total of the possibilities that you have agreed, so we hope you understood this content and liked Gis's explanation, now I'm going to make a calculation here which goes I'm likely to subscribe to my channel and how likely are you to leave a thumbs up for Giz huh, I just want to see! Let's see if this probability is high? Combined people!

So until the next class bye!