The probability of an event characterizes the possibility that it will occur. When we are unsure of the outcome of an experiment, we are talking about the probability that events will happen-the chance they have to happen. Statistics is the branch of mathematics whose object is the study of data from the observation of random phenomena that is to say characterized by chance, uncertainty.
If probabilities are more and more present in the programs, it’s not for nothing. It is because they are so in everyday life! Do not believe that probabilities are useless.
In the world around us, there are many phenomena for which randomness plays an important role. Some are natural like the weather, the meeting of an animal with one of its predators, the location of earthquakes, etc.
Others come from our creations such as games of chance, the risk of having a car accident or falling on an ultra severe corrector on the day of the BAC. By mathematically studying the randomness of these phenomena, we can draw global characteristics to get a better idea of their behavior. Even to try to predict them precisely. That’s what probabilities are for.
The vocabulary to understand the probabilities
As usual, if we want to be able to discuss clearly what we are studying, we must define a clear and unambiguous framework. In other words, to understand probabilities we must understand the specific vocabulary. Let’s go !
Universe: all eventualities
When we want to study a random phenomenon, we will begin by defining its limits. What are we studying and what are the possible situations? It’s the first thing to do. For that, we will limit the framework to the strict minimum.
For example, if you roll a die, there are only 6 possible outcomes, one per face. This is what we will call contingencies. Another example, the day of the second round of the presidential election, there are only 2 eventualities. Either a candidate is elected or it is the other.
What are the Probabilities?
We talked about the framework, what could happen, now we have to talk about probabilities. Yes, because what we want at the beginning, is still understand the probabilities.
So to start, we talk about the probability of an event. If you talk about probas without mentioning the event you consider it will not make sense.
And what is the probability of an event in mathematics? A number between 0 and 1 that represents the chances that this event will occur.
Why are probas always between 0 and 1?
Because it simplifies our life to compare them but not only:
In simple cases like that of the roll, you naturally see that there will be 1 chance out of 6 to fall on the 2 for example. And 1/6 is well understood between 0 and 1. While if I ask you the chances of falling on an 8, you will tell me that there is 0 chance! In other words, the probability of an impossible event is 0.
On the other hand, if I ask you the chances of falling on a 1, a 2, a 3, a 4, a 5 or a 6 when you roll a die, there are 6 chances out of 6. And 6/6 that is 1. In other words, the probability of a certain event is 1.
So you see that the 2 most extreme events have probabilities of 0 (it will never happen) and 1 (it will always happen), all other events will have probas included in 0 and 1.