Hello and welcome back to the class of our course about the complete introduction to data science.
So in this class, this will be our last class about death statistics.
And in today's class, the main topic would be probabilities.
So we are going to talk about what exactly are probabilities, where they're used and some of the formulas
that you guys can find in probability.
We're not going to go too much in depth in those formulas because just the concept of statistics and
probability, just the concept, really could be a complete class of at least forty five hours that
we can talk about, about all the functions that are in play, how to use those functions and many other
things.
So try to be as brief as possible and and give you a brief introduction to this topic.
So let's jump right into it.
So basically what exactly are probabilities in this case?
Probabilities are the measure of likelihood that an event will occur in a random experiment.
So basically, it's just the probability of something happening.
So let's say, for example, you are playing with a one dollar piece of money.
And what are the chances that when true, that piece of money it will it will fall on a hat on the face,
so it will fall on face.
So you will have 50 percent of chances that this piece of money, if you throw it, it falls on face.
So basically, those are the police would simply be the odds of this happening.
In that case, probabilities are used in many, many places, not only in data science.
Well, it's really a huge part of it, but it can be used in many, many places.
So basically it's simply calculating the odds of something happening.
So one of the major places where this is used is casinos.
So basically, when you're going to the casino and let's say you are playing a game, why the casino
always wins because you have statisticians that have studied the game.
They have created a game that gives you an advantage on the long run.
So, yes, sometimes the casino might lose money on the short run.
So you come here, you play, you win, you go home.
But on the long run, on, let's say, you know, one hundred plays, one thousand plays, the casino
will always be positive.
So basically, that's the goal of the casino being positive on the on the long run.
So basically where exactly police are used, it can be used in many places, as I said.
So the first one will be games of chances.
So in this case, everywhere where you need to gamble.
So it could be sports.
It could be I don't know, it could be, for example, casinos.
It could be a lottery.
It could be all the places where you have to gamble.
So once again, if you don't imply a mathematical calculation and you just speculate on a certain outcome,
those well, you will include probabilities.
And if you start calculating and well, including math, including math, it's no longer gambling.
Second place the weather prediction.
So basically, for those who don't know how exactly it works, better prediction.
So you have someone that will analyze what exactly will analyze some some things.
For example, looking at clouds, looking at the sun and some other variables that I know nothing about.
But they will analyze some variables.
And by analyzing those variables, they will be able to make a prediction based on many variables.
Once again, this prediction is never 100 percent sure.
It's only based on past experiments.
This is why the weather is not always accurate, but based on past experiences.
The weatherman is able to say, hey, tomorrow we can we will have a sunny day and we have 30 percent
or 30 percent sure that that it's going to rain once again, just 30 percent.
And once again, it will predict based on different variables.
The third part would be finance.
So for everybody who is speculating on the financial market, probabilities are really a huge part of
it.
So to be able to calculate the risk that the person is taking, so just putting the risk as a number,
it's really important.
Well, putting it any number and understanding it, understanding how much profits you could be able
to make, understanding all the variables that are around financial investments require a lot of public
knowledge through that mathematics, since statistics and probabilities are part of statistics that
are part of mathematics.
Of course, mathematics, well, have a lot of probabilities in them.
It's a part of it.
And finally, any other place where you require that you are required to make provisions and that you
are required to speculate on something that will happen or no say in part, what we are going to talk
about today will be the type of event.
So basically probabilities.
You have two types of events that can happen.
So you have this joint events and once again on joint events, basically a difference between both of
them is that one will include two variables.
Well, the first one with.
So if two events can cannot both happen at the same time, so basically the first one will include that
two events can happen at the same time, and the other one will be able to let you have two events that
happen at the same time.
So if we start with the first event type, so that this joint event so a good example that we can have
is the one that I wrote right here.
So the probability that we get one and two simultaneously by rolling the dice so you have a dice in
your hand and you threw that dice, what are is it possible to have one in two at the same time?
No, it's not possible because you only have one one dice and it's possible to have a one or a two.
So this would be a disjoined event because you can't have those answers at the same time.
But let's say right now you have two doses and you threw them and you show those Dice's and you have
a one and you can have a one and a two at the same time, because the fact that the dice, number one,
falls on one is not dependent on the dice.
Number two, that falls on number one or number two or whatever.
So there is an independence between the two things that are thrown in this case, the dice that are
thrown.
And this independence makes it a non disjoint event.
So basically disjoined if there is a dependence between the two events.
So if we throw one dice, it will have a dependence.
So the fact that it falls on the one make the dice well will create a situation where the dice can't
fall on two because it's already fought on one on one.
But on the non disjoined event, if we truly to dice is the fact that the dice number one falls on the
one makes doesn't make a situation when dice number two can fall on one or two decks, number two will
fall on one or two or whatever.
So there is no dependence between Dice's.
So here you can have an example of it.
So you will have mutually exclusive events that will be disjoined events and you will have not mutually
exclusive events that are nonetheless joint events.
And basically the difference.
Enciso, A and B can't happen at the same time and here, and B can happen at the same time.
So in the non disjoined events, it's possible to have them happening at the same time.
Next thing that we are going to talk about today will be the types of probability.
And basically in this case, we have three types that are very important you're going to talk about.
So you have the marginal probabilities.
We have conditional probabilities and finally we have joint probabilities.
The first one that is the marginal probability is pretty simple to understand.
It's simply the odds or the probabilities that something happens right now or happens at a certain moment,
the moment.
So basically, let's look at this example.
So the probability of drawing a black card in a deck of cards.
So say you have a deck of cards right now and you want to you take a card.
So the probability that this card would be a black card, basically half of the deck is black.
How the deck is red.
So you will have 50 percent of chances of taking away taking out a black card.
So basically, this would be an example of marginal probability, the event, the probability that something
happens right now on the spot.
Second thing would be conditional probability in this case, that will be the probability of an event
occurring when another event has occured.
So basically, let's say something happens.
Let's say you have drawn a certain card.
So like an example right here, you have a king and a deck of cards and then this king.
What are the odds that this king would be, let's say red would be a red card?
So once again, the chances of this king being the red card would be 50 percent, because you have four
kings, you have taken away a king.
And the probability of this king being red would be simply 50 percent, because you have four things
to read to black.
But in the other case, if let's say, for example, you have taken out a red card, what are the odds
that those of this red card is a king?
Well, in this case, it's a bit more different because you have well, you have 52 cards in a deck,
so you will have.
We want you in this case, you will have twenty six cards of each of 13 cards that are red, so the
chances of you having a king in those 13 cards would be one on 13.
So once again, this is a fraction, but it's going to be something like seven percent.
So you will have seven percent of chances that this card that you just took took out would be king.
All right.
So the final one, the joint probability, it's well, looks like the conditional probability you will
see it's pretty much the same thing, but there is a small difference between both of them.
So the joint probability is the reality that two events occur at the same time.
So what are the odds that you drew a one and a half and a deck of cards?
So basically, what are the probabilities that you do a one heart in a deck of cards?
So basically this probability would be one on fifty two because there is just one heart.
So one eight in this case, it's going to be a what ace.
So basically in this case, it's going it's going to be one on 52 because you only have one ace of heart
inside of the deck of cards if the probability of future ace of red.
So in this case, it's going to be one on the twenty six.
So the probability of you drawing the ace a red, it's going to be greater than probability of you drawing
ace.
That is a part.
So basically this is the difference between the conditional and the joint.
So basically the conditional will will happen if an event occurs, the probability that another event
occurs as well.
So this would be the conditional.
So something happens and then you are looking at the probabilities that something else happens.
So it's basically two probabilities and the joint probability, it's like putting those two probabilities
together.
So basically, let's let's take once again this example right here of the king.
Let's say you took a king of your pack of cards.
In the first case, you calculate the stress, the probabilities, a few a king, then you will calculate
the probability of you joining it can't read King.
So in this case that you drew a red card as well, in the joint probability, you will simply calculate
the probability of you drawing a red king.
So this would be just this calculation that will be made.
So this is for the title of the last thing that we are going to think about are the probability distributions.
So once again, this is the birth of the course that takes the most of time because there is a lot and
a lot and a lot of formulas.
They pretty much look like this.
So as you can see, basically what you need to understand, we're not going to go to each of the formulas
well, through each of the functions.
But what you need to understand is that the probability distributions are a function that describes
the likelihood of obtaining a possible value that a random variable can assume based on different criteria.
So basically, you have a situation that happens and you want to calculate the odds of something happening.
So how exactly do you calculated?
So you need to take all the variables in consideration and based on the situation, you will have to
use a certain function.
So you will not use that geometrical function at the same time that you will use the B well, the Benally
function, for example, or the binomial function or the plus one function, everything all those functions
are based on different situations and are based on different type of events.
So let's say, for example, if you have a situation where where you, I don't know, draw cards, for
example, from a deck and you put them back inside of the deck and you want to have the probability
of you drawing two times the same card so will not use the same function that if you don't put back
the cards in the deck.
So basically you will use two different functions, because in the first situation, you took the cards
from the deck and each time you put them back inside of the deck and in the same situation, you didn't
you didn't put the cards back inside the deck.
So there is depending of the situation, you will use different probability distributions.
So different functions.
So this is what you guys need to understand about probability distributions once again.
There is a lot of them.
And to become, well, more advanced and understand them all, you need to practice.
If you guys are interested, I highly suggest you to just take a statistics course and you will have
everything that you need instead of it because, well, especially if you want to know a bit more about
those functions.
So basically what we talked about inside of the scores are probabilities in.
Well, we talked about probabilities.
We talked about types of event.
We talked about type different types of probabilities and finally probability distributions that are
this part of the course.
So this, as I said, the statistical.
Part of the scores can easily be done in at least two university level courses, so it's really complicated.
I try to make it as easy as possible for you guys to understand it.
So once again, this is just a an introduction to it.
So I hope you guys liked it.
And if you liked, well, all the studies, if you like the statistical part and want to get well to
understand it a bit better, I highly suggest you to take a statistical course.
We're just to practice a little bit and you'll see it's not that hard.
It's not that complicated to understand.
It's just a question of practice.
So that's it for this last course about statistics and see in our next class.