Probability is the chance that something can happen. An event is one or more of the responses to that something happening.
Experiment: the activity that produces events.
Mutually exclusive event:
They are those events in which the characteristic that they CANNOT happen at the same time is fulfilled.
Not mutually exclusive event:
They are those events that CAN happen at the SAME TIME.
Example:
A person has a coin and in a few moments he is going to throw it in the air and of course there is uncertainty about the result of such action, let's see the interpretation of each of the terms.
Experiment: tossing a coin.
Event: Each of the responses in this activity, event one will be Sol and event two will be Eagle.
The set of all possible outcomes of an experiment is called the sample space.
It is represented by the letter S.
S = Eagle, Sun.
Questions:
Are Eagle and Sun mutually exclusive events?
Yes, because only one side of the coin can come out, either sun or eagle, but not both.
EQUIPROBABILITY:
The concept of equiprobability suggests that if there is no reason to favor any of the possible results of an experiment, then the results should be considered EQUALLY LIKELY to occur.
P (eagle) = P (sun)
MARGINAL PROBABILITY FORMULA:
P (EVENT) = NUMBER OF FAVORABLE CASES FOR THE EVENT / TOTAL NUMBER OF EXPERIMENT RESULTS.
Example: What is the probability that an eagle appears in a coin toss?
P (eagle) = 1 (How many eagles can fall in that shot?) / 2 (How many sides or faces does the coin have?).
P (eagle) = ½ = 0.5 = 50% the probability can be expressed in decimals, percentages or fractions.
Let's look at the example on a die.
The sample space will be:
S = 1,2,3,4,5,6
What is the probability that an even number will fall from that die?
Let's select the pairs.
S = 1,2,3,4,5,6
We have that the probability is:
P (given pairs) = 3 (three number that are even, therefore there are three possibilities that it is even) / 6 (the number of elements of my space)
P (given pairs) = 3/6 = 0.5 = 50%
What is the probability that the number 3 of that die will fall?
P (# 3) = 1 (in the dice there is only a number 3) / 6 (total elements of my space)
P (# 3) = 1/6 = 0.16 = 16%.
PROBABILITY UNDER CONDITIONS OF STATISTICAL INDEPENDENCE.
When two events occur the result of the first MAY OR MAY NOT have an effect on the result of the second event, that is, the events can be either dependent or independent.
STATISTICALLY INDEPENDENT EVENTS.
They are those in which the occurrence of an event has NO effect on the probability of the occurrence of any other event.
There are 3 types of probability under the condition of statistical independence:
Marginal: Individual probability means that only one event can take place.
P (SOL) = ½
Joint: It is the probability that 2 or more independent events occur together or in succession, it is the product of their marginal probabilities.
Formula:
P (AÇB) = P (A) * P (B)
P (AÇB) = LIKELY THAT EVENTS A AND B WILL OCCUR TOGETHER OR IN SUCCESSION.
P (A) = MARGINAL PROBABILITY OF A.
P (B) = MARGINAL PROBABILITY OF B.
Example: If we flip a coin 2 times, what is the probability of getting 2 eagles (eagle and eagle)?
S = Coin 1 eagle, sol.
Coin 2 eagle, sol.
P (eagle) P (eagle) * P (eagle) = ½ * ½ = ¼
Conditional:
It is one in which the probability of one event is conditioned to the occurrence of another event.
P (B½A) = P (B)
It reads: "the probability of event B if the event has occurred".
In the following video course (Educatina) a brief introduction to the concept of probability is made, you will learn how probability is calculated and other basic concepts.
