Probability
Here you have different experiments to practice
Sommario
- Experiments
- COIN TOSS (I)
- COIN TOSS (II)
- Throwing a dice
- Horse race
- Horse race (sum)
- Horse race (subtraction)
- Primitiva
- Dartboard
- Rigged die
- Sample space
- Sample space
- Laplace's Rule
- Laplace rule (1): Tossing coins
- Laplace Rule (2): Throwing a die
- Laplace rule (3): Urn extraction (I)
- Laplace Rule (4):Urn extraction (II)
- Urns
- Urn (I)
- Urn (II)
- Urn (III)
- Urn (IV)
- Urn (random)
- Tree diagram problems
- Árbol (I) _ Dos ramas y dos extracciones CON reemplazamiento
- Árbol (II) : Dos ramas y dos extracciones sin reemplazamiento
- Árbol (III) tres ramas CON reemplazamiento
- Árbol (IV) tres ramas SIN reemplazamiento
COIN TOSS (I)
Random experiments. Probability introduction
You can simulate what could happen if you toss a coin several times. Count the number of heads and tails that would come up on those tosses. You can repeat as many times as you want
Activity proposal
- Each student performs their own experimetns and compares with their classmates[br]- You can add all the results and see if it changes substantially[br]- Make graphs to compare to the results
Sample space
Probability
Here are 3 of the most classic examples of sample spaces, referring to well-known experiments:[br]- Coin toss[br]- Throwing a 6-sided die[br]- Extraction of a card from a Spanish deck[br]Let us remember that the sample space is all the possible results of an experiment.[br]It is generally described with the elementary events and from there the rest of the possibilities are built.
Laplace rule (1): Tossing coins
Probabilty
Lâplace's rule helps us to calculate the probability of an event, based on the sample space, since we have to perform a count. The rule says:[br][math]P\left(A\right)=\frac{Favour-Outomes}{Posible-Outcomes}[/math] That is to say, the probability of an event is the proportion between the number of favour outcomes of its occurrence, divided by the total number of outcomes of the experiment.[br]As long as we can describe and "count" the elements or outcomes of the sample space, we can easily apply this rule.
Proposal
-Check the first example[br]- Check the sample space[br]-Check that the rule is verify with an example[br]- Repeat it for similar examples
Urn (I)
Probability introduction
We will try to guess the proportion of balls of each color in each urn. We don't know the number of balls or colors. To guess the composition you have to make extractions and write down the results, and analyze the relationship between them: if there is the same number of balls of each colour, one doubles the other,...[br]Calculating the proportions, you should estimate the theoretical probability. A minimum number of extractions has been set that can be varied so that the result is not revealed the first time. There is a sheet that you can use in class for the students.[br]
Plantilla de recogida de información
Activity proposal
- Extractions are made and the results are noted[br]- When we believe that we can deduce the probability, we write it on the sheet[br]- We repeat the process with other urns[br]- We collect information from other students or groups
Árbol (I) _ Dos ramas y dos extracciones CON reemplazamiento
Probabilidad
En este ejemplo se trabaja con un problema que requiere la técnica de árbol. Necesitaremos, en cada extracción, saber la probabilidad de cada opción. Una vez que lo sepamos podremos construir el árbol y contestar a cualquier pregunta que nos hagan
Propuesta
- Analizar las probabilidades de cada suceso y comprobar que sale lo que esperamos[br]- Calcula la probabilidad de que salgan las dos verde [br]- Calcula la probabilidad de que salga una de cada color[br]- Calcula la probabilidad de que salga del mismo color