We begin by reviewing some concepts of probability.
Sample space
The sample space is the set of all the possible results of a random experiment and is usually represented as E (or as omega, Ω, of the Greek alphabet).
For example, when we throw a coin, what are all the possible outcomes we can get? Face it or cross it, right? In total there are two possible results, so the sample space has 2 elements.
E = {face, cross}
And if we roll a die, we have a total of 6 possible outcomes that can come out. Therefore, the sample space would be 6 elements.
E = {1, 2, 3, 4, 5, 6}.
Event
An event is any subset of the sample space. For example, "take off" in the toss of a coin, "take out number 5" or "take out a prime number" in the throw of a die are events.
Let's see what the sample space would be in the first section of our exercise.
What are all the possible outcomes? We refer to the numbers of the balls, which are the numbers from 11 to 20.
Our sample space has 10 elements:
E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
And the event they ask us about is "get a prime number."
Now, how do we calculate the probability of this event?
When all elementary events have the same probability of occurring, the probability of any event A is defined as the quotient between the number of favorable cases and the number of possible cases. This is the Law of Laplace.
Probability
In the example of throwing a coin, the elementary events would be: "Take out a cross" or "Draw a face". If the coin is not tricked, the probability of each elementary event occurring is the same. Therefore, the probability of the cross coming out is 1/2.
Here there are some activities to practice that:
http://recursostic.educacion.es/multidisciplinar/itfor/web/sites/default/files/recursos/elazarylaprobabilidad/html/actividad_1_probabilidades.html
Sample space
The sample space is the set of all the possible results of a random experiment and is usually represented as E (or as omega, Ω, of the Greek alphabet).
For example, when we throw a coin, what are all the possible outcomes we can get? Face it or cross it, right? In total there are two possible results, so the sample space has 2 elements.
E = {face, cross}
And if we roll a die, we have a total of 6 possible outcomes that can come out. Therefore, the sample space would be 6 elements.
E = {1, 2, 3, 4, 5, 6}.
Event
An event is any subset of the sample space. For example, "take off" in the toss of a coin, "take out number 5" or "take out a prime number" in the throw of a die are events.
Let's see what the sample space would be in the first section of our exercise.
What are all the possible outcomes? We refer to the numbers of the balls, which are the numbers from 11 to 20.
Our sample space has 10 elements:
E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
And the event they ask us about is "get a prime number."
Now, how do we calculate the probability of this event?
When all elementary events have the same probability of occurring, the probability of any event A is defined as the quotient between the number of favorable cases and the number of possible cases. This is the Law of Laplace.
Probability
In the example of throwing a coin, the elementary events would be: "Take out a cross" or "Draw a face". If the coin is not tricked, the probability of each elementary event occurring is the same. Therefore, the probability of the cross coming out is 1/2.
Here there are some activities to practice that:
http://recursostic.educacion.es/multidisciplinar/itfor/web/sites/default/files/recursos/elazarylaprobabilidad/html/actividad_1_probabilidades.html
Comentarios
Publicar un comentario