The classic probability it is a particular case of the calculation of the probability of an event. To understand this concept it is necessary to first understand what the probability of an event is.
The probability measures how likely it is that an event will happen or not. The probability of any event is a real number that is between 0 and 1, both inclusive.
If the probability of an event happening is 0 it means that it is certain that this event will not happen.
On the contrary, if the probability of an event happening is 1, then it is 100% sure that the event will happen.
Probability of an event
It was already mentioned that the probability of an event happening is a number between 0 and 1. If the number is close to zero, it means that the event is unlikely to happen.
Equivalently, if the number is close to 1 then it is quite likely that the event will happen.
In addition, the probability that an event will happen plus the probability that an event does not happen is always equal to 1.
How is the probability of an event calculated?
First the event is defined and all the possible cases, then the favorable cases are counted; that is, the cases that interest them to happen.
The probability of said event"P (E)"is equal to the number of favorable cases (CF), divided among all possible cases (CP). That is to say:
P (E) = CF / CP
For example, you have a coin such that the sides of the coin are expensive and seal. The event is to throw the coin and the result is expensive.
Since the currency has two possible outcomes but only one of them is favorable, then the probability that when the coin is tossed the result is expensive is 1/2.
Classic probability
The classic probability is that in which all possible cases of an event have the same probability of occurring.
According to the above definition, the coin toss event is an example of a classical probability, since the probability of the result being expensive or being a stamp is equal to 1/2.
The 3 most representative classical probability exercises
First exercise
In a box there is a blue ball, a green ball, a red ball, a yellow ball and a black one. What is the probability that, when the eyes are closed with a ball from the box, it is yellow?
Solution
The event"E"is to take a ball out of the box with the eyes closed (if it is done with the eyes open the probability is 1) and that it is yellow.
There is only one favorable case, since there is only one yellow ball. The possible cases are 5, since there are 5 balls in the box.
Therefore, the probability of event"E"is equal to P (E) = 1/5.
As can be seen, if the event is to take a blue, green, red or black ball, the probability will also be equal to 1/5. Therefore, this is an example of classical probability.
Observation
If there were 2 yellow balls in the box then P (E) = 2/6 = 1/3, while the probability of drawing a blue, green, red or black ball would have been equal to 1/6.
Since not all events have the same probability, then this is not an example of classical probability.
Second Exercise
What is the probability that, when rolling a die, the result obtained is equal to 5?
Solution
A die has 6 faces, each with a different number (1,2,3,4,5,6). Therefore, there are 6 possible cases and only one case is favorable.
So, the probability that when the die is thrown is 5 is equal to 1/6.
Again, the probability of obtaining any other die result is also equal to 1/6.
Third Exercise
In a classroom there are 8 boys and 8 girls. If the teacher chooses a student from her classroom at random, what is the probability that the chosen student is a girl?
Solution
The"E"event is choosing a student at random. In total there are 16 students, but since you want to choose a girl, then there are 8 favorable cases. Therefore P (E) = 8/16 = 1/2.
Also in this example, the probability of choosing a child is 8/16 = 1/2.
That is, it is as likely that the chosen student is a girl as a child.
References
- Bellhouse, D. R. (2011). Abraham De Moivre: Setting the Stage for Classical Probability and Its Applications. CRC Press.
- Cifuentes, J. F. (2002). Introduction to the Theory of Probability. Univ. National of Colombia.
- Daston, L. (1995). Classical Probability in the Enlightenment. Princeton University Press.
- Larson, H. J. (1978). Introduction to the theory of probabilities and statistical inference. Editorial Limusa.
- Martel, P. J., & Vegas, F. J. (1996). Probability and mathematical statistics: applications in clinical practice and health management. Ediciones Díaz de Santos.
- Vázquez, A. L., & Ortiz, F. J. (2005). Statistical methods to measure, describe and control variability. Ed. University of Cantabria.
- Vázquez, S. G. (2009). Mathematics Manual for access to the University. Editorial Center of Studies Ramon Areces SA.