Build the Models 🚂



## Warming Up
Welcome to Hands-on Probability! Here we'll try to use an interactive way to help you to learn Probability.   

Before any blah-blah-blah, how about have a fair question with a fair dice?




We play a fair dice 🎲 . What's the probability of getting a six?
<MCQuest correct="A" totalAttempts="2">
* $\frac{1}{6}$
* $\frac{1}{3}$
* $\frac{1}{2}$
* $1$
</MCQuest>


We play a fair dice 🎲 . What's the probability of getting a six?


* $\frac{1}{6}$
* $\frac{1}{3}$
* $\frac{1}{2}$
* $1$




## Experiment

Processes, like playing a dice, flipping a coin, forecasting the weather, are called experiments.

<Definition>
**Experiment**

An experiment is any process, real or hypothetical, in which the possible outcomes can be identified ahead of time.  

(from "Probability and Statistics")
</Definition>

<Idea>
Deterministic processes are also experiments.
</Idea>


## Experiment

Processes, like playing a dice, flipping a coin, forecasting the weather, are called experiments.

<Definition>
**Experiment**

An experiment is any process, real or hypothetical, in which the possible outcomes can be identified ahead of time.  

(from "Probability and Statistics")
</Definition>


**Experiment**

An experiment is any process, real or hypothetical, in which the possible outcomes can be identified ahead of time.  

(from "Probability and Statistics")


<Idea>
Deterministic processes are also experiments.
</Idea>


Deterministic processes are also experiments.




When you submit a true for this question, you will always get a success result. Is it an experiment?

<MCQuest correct="A" totalAttempts="1">
* True
* False
</MCQuest>


When you submit a true for this question, you will always get a success result. Is it an experiment?

<MCQuest correct="A" totalAttempts="1">
* True
* False
</MCQuest>



## Build the Model
Let's build the probability model of playing a dice. Or, for any experiment.  

"But wait, what do you mean by building models?"  
Great question. Building mathematical models are the heart of study of mathematics:

<Idea>
Building mathematical models, is to use mathematical words and build some general concepts, to describe the informations of some phenomenon.
</Idea>

So, there are two parts for building models:
1. Find the informations you want to describe
2. Use mathematical words to define some concepts to describe

Now let's focus on the first part.

## Find the Informations You Want to Describe
Back to our **Rolling a Dice** 🎲 , what informations are important to us to describe?


## Build the Model
Let's build the probability model of playing a dice. Or, for any experiment.  

"But wait, what do you mean by building models?"  
Great question. Building mathematical models are the heart of study of mathematics:

<Idea>
Building mathematical models, is to use mathematical words and build some general concepts, to describe the informations of some phenomenon.
</Idea>


Building mathematical models, is to use mathematical words and build some general concepts, to describe the informations of some phenomenon.


So, there are two parts for building models:
1. Find the informations you want to describe
2. Use mathematical words to define some concepts to describe

Now let's focus on the first part.

## Find the Informations You Want to Describe
Back to our **Rolling a Dice** 🎲 , what informations are important to us to describe?



For information are important for a probability experiment?  
This is an opinion question, feel free to take a guess.

<MCQuest correct="C" totalAttempts="2">
* All possible results. For the rolling dice example, the result can be 1, 2, 3, 4, 5, and 6.
* Likelihood for each result.
* Both.
</MCQuest>


For information are important for a probability experiment?  
This is an opinion question, feel free to take a guess.

<MCQuest correct="C" totalAttempts="2">
* All possible results. For the rolling dice example, the result can be 1, 2, 3, 4, 5, and 6.
* Likelihood for each result.
* Both.
</MCQuest>


* All possible results. For the rolling dice example, the result can be 1, 2, 3, 4, 5, and 6.
* Likelihood for each result.
* Both.




Okay, the first part is done.
Now we need to use mathematical words to describe these informations:
1. All possible results, aka, outcomes.
2. The probability law for the experiment.

In next section, you will meet the Sample Space, which is a mathematical way to tell us about all possible outcomes of an experiment.
