Regla de LAPLACE 🎲 Explicada con EJEMPLOS
rule|of|Laplace|explained|with|examples
LAPLACE 규칙 🎲 예제로 설명
Правило ЛАПЛАСА 🎲 Объясняется ПРИМЕРАМИ
LAPLACE-regeln 🎲 Förklarad med EXEMPEL
LAPLACE's Rule 🎲 Explained with EXAMPLES
cada atardecer si miramos al oeste vemos
every|sunset|if|we look|to the|west|we see
every sunset if we look to the west we see
como el sol se oculta tras esas montañas
how|the|sun|itself|it hides|behind|those|mountains
how the sun hides behind those mountains
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si calentamos agua hasta 100 grados
if|we heat|water|up to|degrees
if we heat water to 100 degrees
centígrados siempre hierve ¡Ay me quemo!
Celsius|always|it boils|oh|myself|I burn
Celsius it always boils! Ouch, I burn!
Y si suelto esta manzana siempre cae ¡Ay!
and|if|I let go|this|apple|always|it falls|oh
And if I drop this apple it always falls! Ouch!
Pero si lanzamos esta moneda al aire
but|if|we toss|this|coin|to the|air
But if we toss this coin in the air
a veces obtendremos cara, a veces
at|times|we will obtain|face|at|times
sometimes we will get heads, sometimes
obtendremos cruz. Si tiramos este dado
we will obtain|cross|if|we throw|this|die
we will get tails. If we roll this die
tampoco sabemos qué número va a salir.
neither|we know|what|number|it is going|to|to come out
we also don't know what number will come up.
Decimos que un experimento es
we say|that|an|experiment|it is
We say that an experiment is
determinista cuando se puede predecir su
deterministic|when|itself|it can|to predict|its
deterministic when its
resultado antes de realizarlo.
result|before|of|to carry it out
outcome can be predicted before performing it.
Por ejemplo, observar el atardecer hacia el
for|example|to observe|the|sunset|towards|the
For example, observing the sunset towards the
oeste siempre termina con el sol
west always ends with the sun
poniéndose; calentar agua hasta 100
putting on|to heat|water|up to
putting on; heating water to 100
grados centígrados
degrees|Celsius
degrees Celsius
siempre termina con el agua hirviendo;
always|it ends|with|the|water|boiling
always ends with the water boiling;
dejar caer una manzana al vacío siempre
to let|to fall|an|apple|to the|vacuum|always
dropping an apple in a vacuum always
termina con la manzana en el suelo.
it ends|with|the|apple|on|the|ground
ends with the apple on the ground.
Por otra parte se dice que un experimento es
on|another|part|itself|it says|that|an|experiment|it is
On the other hand, it is said that an experiment is
aleatorio si al repetirlo varias veces
random|if|upon|repeating it|several|times
random if repeating it several times
en las mismas condiciones se pueden
in|the|same|conditions|itself|they can
under the same conditions can yield
obtener resultados diferentes.
to obtain|results|different
get different results.
Por ejemplo, al lanzar una moneda podemos
for|example|upon|to toss|a|coin|we can
For example, when flipping a coin we can
obtener cara o cruz. Si tiramos un dado
to obtain|heads|or|tails|if|we throw|a|die
get heads or tails. If we roll a die
podemos obtener seis resultados
we can|to obtain|six|results
we can get six results.
diferentes.
different
different.
¿Merece la pena aplicar el razonamiento
does it deserve|the|worth|||
Is it worth applying reasoning
matemático a experimentos aleatorios en
mathematical to random experiments in
los que el azar juega un papel esencial?
which|that|the|chance|it plays|a|role|essential
which chance plays an essential role?
¿No son las matemáticas una
not|they are|the|mathematics|a
Aren't mathematics an
ciencia exacta? ¿De verdad podemos dar una
science|exact|||||
exact science? Can we really provide a
base matemática al azar?
mathematical basis for chance?
En el verano de 1.654 los matemáticos
In the summer of 1654, mathematicians
franceses Pierre de Fermat y Blaise Pascal
French|Pierre|of|Fermat|and|Blaise|Pascal
Frenchmen Pierre de Fermat and Blaise Pascal
pensaron que esto era posible e
they thought|that|this|it was|possible|and
thought this was possible and
iniciaron una intensa correspondencia.
they initiated|an|intense|correspondence
started an intense correspondence.
Otros matemáticos importantes se unieron
other|mathematicians|important|themselves|they joined
Other important mathematicians joined in.
a la fiesta como el holandés Christiaan
to|the|party|like|the|Dutch|Christiaan
to the party like the Dutchman Christiaan
Huygens y posteriormente los suizos
Huygens|and|subsequently|the|Swiss
Huygens and later the Swiss
Jacob en Bernoulli y Leonard Euler y el
Jacob|in|Bernoulli|and|Leonard|Euler|and|the
Jacob Bernoulli and Leonard Euler and the
francés Pierre-Simon de Laplace de cuya
French|||of|Laplace|of|whose
Frenchman Pierre-Simon de Laplace of whom
regla vamos a hablar en este vídeo.
rule|we are going|to|to talk|in|this|video
rule we are going to talk about in this video.
¡Empezamos!
we start
Let's get started!
La probabilidad de un suceso, como por
the|probability|of|a|event|like|for
The probability of an event, such as
ejemplo, que salga cara al tirar una
for example, getting heads when flipping a
moneda es un número entre 0 y 1.
coin|it is|a|number|between|and
currency is a number between 0 and 1.
En este caso 0,5 que podemos escribir
in|this|case|that|we can|to write
In this case 0.5 which we can write
como un porcentaje desplazando la coma
as|a|percentage|shifting|the|comma
as a percentage by moving the decimal
dos lugares. Esto es, la probabilidad de
two|places|this|it is|the|probability|of
two places. That is, the probability of
obtener una cara al lanzar una moneda es
to obtain|a|heads|when|to flip|a|coin|it is
getting heads when flipping a coin is
del 50% pero ¿qué quiere decir que la
of the|but|what|it wants|to say|that|the
50% but what does it mean that the
probabilidad de este suceso es del 50% ?
probability|of|this|event|it is|of the
probability of this event is 50%?
El significado de este porcentaje es que
the|meaning|of|this|percentage|it is|that
The meaning of this percentage is that
si lanzamos la moneda un número grande
if|we launch|the|coin|a|number|large
if we flip the coin a large number
de veces la frecuencia con la que
of|times|the|frequency|with|the|that
of times the frequency with which
aparecerá cara será de un 50%.
it will appear|heads|it will be|of|a
heads will appear will be 50%.
A ver, lanzó la moneda diez veces y obtengo
let's|see|she launched|the|coin|ten|times|and|I obtain
Let's see, I flipped the coin ten times and I got
cuatro caras y seis cruces, esto es, un
four|faces|and|six|crosses|this|it is|a
four heads and six tails, that is, a
40% de caras.
of|faces
40% of heads.
¿Qué está pasando?¿No debería salir 50%?
what|it is|happening|not|it should|to come out
What's happening? Shouldn't it be 50%?
Básicamente lo que está sucediendo es
basically|what|that|it is|happening|it is
Basically what is happening is
que 10 no es un número muy grande.
that|not|it is|a|number|very|large
that 10 is not a very large number.
Si lanzamos la moneda 100 veces obtendremos
if|we launch|the|coin|times|we will obtain
If we flip the coin 100 times we will get
algo más ajustado. Por ejemplo, me han
something|more|adjusted|for|example|to me|they have
something more accurate. For example, I got
salido 52 caras y 48 cruces, esto es, un
come out|heads|and|tails|this|it is|a
52 heads and 48 tails, that is, a
52% de caras. Si lanzáramos la moneda mil
of|heads|if|we were to toss|the|coin|thousand
52% of heads. If we were to flip the coin a thousand
veces además de cansados veríamos que el
times|in addition|to|tired|we would see|that|the
times, besides being tired, we would see that the
porcentaje se parece cada vez más al 50%.
percentage|itself|it seems|every|time|more|to the
percentage increasingly resembles 50%.
Por ejemplo, 496 frente a 504, esto es,
for|example|against|to|this|is
For example, 496 versus 504, this is,
49,6% de caras.
of|heads
49.6% heads.
Si pudiéramos repetir el experimento
if|we could|to repeat|the|experiment
If we could repeat the experiment
infinitas veces la proporción de caras
infinite|times|the|proportion|of|heads
infinitely many times, the proportion of heads
sería del 50%. Pero, ¿esto no parece muy
it would be|of the|but|this|not|it seems|very
would be 50%. But, doesn't this seem very
matemático? ¿Cómo puedo calcular la
mathematic|how|I can|to calculate|the
mathematician? How can I calculate the
probabilidad de un suceso si no puedo
probability|of|a|event|if|not|I can
probability of an event if I cannot
hacer un experimento infinitas veces?
to do|an|experiment|infinite|times
perform an experiment infinitely many times?
Para eso tenemos la REGLA DE LAPLACE
for|that|we have|the|rule|of|Laplace
For that, we have the LAPLACE'S RULE
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si tenemos un experimento aleatorio en
if|we have|an|experiment|random|in
if we have a random experiment in
el que todos los sucesos elementales
the|that|all|the|events|elemental
which all the elementary events
tienen la misma probabilidad decimos que
they have|the|same|probability|we say|that
have the same probability we say that
estos sucesos son equiprobables.
these|events|they are|equally probable
these events are equally probable.
Por ejemplo, la probabilidad de cara y cruz
for|example|the|probability|of|heads|and|tails
For example, the probability of heads and tails
al tirar una moneda es la misma y por
upon|throwing|a|coin|it is|the|same|and|for
when flipping a coin is the same and therefore
tanto obtener cara y obtener cruz son
therefore|to obtain|heads|and|to obtain|tails|they are
getting heads and getting tails are
sucesos equiprobables. La probabilidad
events|equiprobable|the|probability
equally likely events. The probability
al lanzar un dado de cada uno de sus
upon|to roll|a|die|of|each|one|of|its
when rolling a die of each of its
lados también es la misma y por tanto
sides is also the same and therefore
los sucesos sacar un 1, sacar un 2,
the events of rolling a 1, rolling a 2,
etcétera son sucesos equiprobables.
etcetera|they are|events|equally probable
etcetera are equally probable events.
La regla de Laplace afirma que en un
the|rule|of|Laplace|it states|that|in|a
The Laplace rule states that in a
experimento aleatorio cuyos sucesos
random experiment whose elementary events
elementales son equiprobables la
are equally probable the
probabilidad de un suceso A
probability|of|a|event|A
probability of an event A
se calcula por la fórmula número de
itself|it calculates|by|the|formula|number|of
is calculated by the formula number of
casos favorables al suceso A, dividido
cases|favorable|to the|event|A|divided
favorable cases for event A, divided
entre el número de casos posibles.
by|the|number|of|cases|possible
by the number of possible cases.
Por ejemplo, trivialmente la probabilidad
for|example|trivially|the|probability
For example, trivially the probability
de obtener un 4 al lanzar un dado es
of|to obtain|a|upon|to throw|a|die|it is
of rolling a 4 when throwing a die is
número de casos favorables al suceso
number|of|cases|favorable|to the|event
the number of favorable cases for the event
sacar un 4, esto es, un caso. Dividido
to roll|a|this|it is|a|case|divided
of rolling a 4, that is, one case. Divided
entre el número de casos posibles,
between|the|number|of|cases|possible
among the number of possible cases,
esto es, 6 casos. Por tanto, obtenemos una
this|it is|cases|for|so|we obtain|a
that is, 6 cases. Therefore, we obtain a
probabilidad de un sexto que dividiendo
probability|of|a|sixth|that|dividing
probability of one sixth by dividing
y desplazando la coma dos lugares a la
and|shifting|the|decimal point|two|places|to|the
and moving the decimal point two places to the
derecha nos da un
right|us|it gives|a
right gives us a
16,6 periódico por ciento ciento.
repeating|by|hundred|
16.6 percent.
¿Cuál es la probabilidad del suceso B que
what|is|the|probability|of the|event|B|that
What is the probability of event B which
consiste en sacar un número par al
it consists|in|to draw|a|number|even|to the
consists of drawing an even number at
lanzar un dado?
to roll|a|die
roll a die?
la probabilidad de B se calculará como
the|probability|of|B|itself|it will calculate|as
the probability of B will be calculated as
el número de casos favorables al suceso B,
the|number|of|cases|favorable|to the|event|B
the number of favorable cases for event B,
que son el 2 el 4 y el 6, esto es,
that|they are|the|the|and|the|this|is
which are 2, 4, and 6, that is,
3 casos. Dividido entre el número de casos
cases|divided|by|the|number|of|cases
3 cases. Divided by the number of cases
posibles que es 6 y obtenemos una
possible|that|it is|and|we obtain|a
possible which is 6 and we obtain a
probabilidad de 3 sextos que es igual a
probability|of|sixths|that|it is|equal|to
probability of 3 sixths which is equal to
0,5 que visto como porcentaje es el 50%
which|seen|as|percentage|it is|the
0.5 which seen as a percentage is 50%
¡Claro! la mitad de las veces saldrá par y
of course|the|half|of|the|times|it will come out|even|and
Of course! Half of the time it will come out even and
la mitad de las veces impar si lanzamos
the|half|of|the|times|odd|if|we throw
half of the time odd if we roll
el dado un número grande de veces.
the|die|a|number|large|of|times
the die a large number of times.
Pero para terminar este vídeo os propongo un
but|to|to finish|this|video|you|I propose|a
But to finish this video, I propose a
ejercicio un poco más complicado:
exercise|a|a little|more|complicated
a slightly more complicated exercise:
si nuestro experimento consiste en lanzar
if|our|experiment|it consists|in|to throw
if our experiment consists of rolling
dos dados ¿Cuál es la probabilidad de que
two|dice|what|is|the|probability|of|that
two dice, what is the probability that
la suma de los números obtenidos sea 8?
the|sum|of|the|numbers|obtained|to be
the sum of the numbers obtained is 8?
Para determinar dicha probabilidad
to|determine|that|probability
To determine that probability
utilizando la regla de Laplace vamos a
using|the|rule|of|Laplace|we are going|to
using Laplace's rule we are going to
empezar viendo cuántos casos posibles
to start|seeing|how many|cases|possible
start by looking at how many possible cases
tenemos en este experimento: El primer
we have|in|this|experiment|the|first
we have in this experiment: The first
dado tiene seis posibilidades diferentes
die|it has|six|possibilities|different
a die has six different possibilities
y el segundo otras seis por tanto
and|the|second|other|six|for|therefore
and the second has another six, therefore
tendremos en total seis por seis igual a
we will have|in|total|six|times|six|equal|to
we will have a total of six times six equals
36 posibilidades. En efecto, si el primer
possibilities|in|effect|if|the|first
36 possibilities. Indeed, if the first
dado es 1 el segundo puede ser 1, 2, 3, 4, 5 o 6.
die|it is|the|second|it can|to be|or
if the first die is 1 the second can be 1, 2, 3, 4, 5 or 6.
Si el primer dado es un 2
if|the|first|die|it is|a
If the first die is a 2
el segundo puede ser de nuevo
the|second|it can|to be|of|again
the second can be again
1, 2, 3, 4, 5 o 6. Lo mismo
or|the|same
1, 2, 3, 4, 5 or 6. The same
sucede con un 3, 4, 5 o 6
it happens|with|a|or
it happens with a 3, 4, 5, or 6
en el primer dado y al final tenemos
in|the|first|die|and|at the|end|we have
on the first die and in the end we have
todas las posibilidades en una tabla de
all|the|possibilities|in|a|table|of
all the possibilities in a table of
seis filas y seis columnas, esto es,
six|rows|and|six|columns|this|it is
six rows and six columns, that is,
de 36 casillas
of|boxes
of 36 boxes
¿Cuál es el número de casos favorables al
what|is|the|number|of|cases|favorable|to the
What is the number of favorable cases for
suceso la suma de los dados es 8?
event|the|sum|of|the|dice|is
the event that the sum of the dice is 8?
con 1 en el primer dado no hay ninguna
with|in|the|first|die|not|there are|any
with 1 on the first die there are none
opción pues lo máximo que suman es 1 + 6
option|because|the|maximum|that|they sum|it is
option since the maximum they add up to is 1 + 6
igual a 7 pero con un 2 en el primer
equal|to|but|with|a|in|the|first
equal to 7 but with a 2 on the first
dado y 6 en el segundo sumamos 8 y con
die|and|in|the|second|we sum|and|with
die and 6 on the second we add 8 and with
un 3 en el primero y 5 en el segundo y
a|in|the|first|and|in|the|second|
a 3 on the first and 5 on the second and
con un 4 en el primero y 4 en el segundo
with|a|in|the|first|and|in|the|second
with a 4 in the first and 4 in the second
y con 5 y 3 y con 6 y 2. En definitiva, la
and|with|and|and|with|and|in|definitive|the
and with 5 and 3 and with 6 and 2. In short, the
probabilidad del suceso sumar 8 es igual
probability|of the|event|to sum|it is|equal
probability of the event summing to 8 is equal
al número de casos favorables, esto es, 5
to the|number|of|cases|favorable|this|it is
to the number of favorable cases, that is, 5
dividido entre el número de casos
divided|by|the|number|of|cases
divided by the number of cases
posibles que era 36. Hemos obtenido por
possible|that|it was|we have|obtained|by
possible which was 36. We have obtained therefore a
tanto una probabilidad de cinco partido
so|a|probability|of|five|divided
probability of five divided
por 36 que es 0.138 periódico o visto
|that|it is|repeating|or|seen
by 36 which is 0.138 recurring or seen
como porcentaje el 13,8 periódico por
as|percentage|the|repeating|by
as a percentage 13.8 recurring percent
ciento.
hundred
.
Esta regla tan sencilla nos será de
this|rule|so|simple|to us|it will be|of
This simple rule will be very useful for us to learn in the coming
mucha utilidad para aprender en próximos
a lot of|utility|to|to learn|in|upcoming
vídeos herramientas cada vez más
videos|tools|each|time|more
videos tools increasingly
sofisticadas para calcular
sophisticated|to|to calculate
sophisticated for calculating
probabilidades ¡Hasta luego!
probabilities|until|later
probabilities Goodbye!
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PAR_TRANS:gpt-4o-mini=2.64 PAR_CWT:At8odHUl=3.48
en:At8odHUl
openai.2025-02-07
ai_request(all=84 err=0.00%) translation(all=168 err=0.60%) cwt(all=1021 err=6.17%)
