Contenido del Curso

Probability Theory Basics

1. Basic Concepts of Probability Theory

Stochastic Experiment and Random Event Probability and It's Properties Geometrical Probability Challenge: Solving the Task Using Geometric Probability Independence and Incompatibility of Random Events Conditional Probability

2. Probability of Complex Events

Inclusion-Exclusion Principle Challenge: Solving the Task Using Inclusion-Exclusion Principle The Multiplication Rule of Probability Law of Total Probability Bayes' Theorem Challenge: Solving the Task Using Bayes' Theorem

3. Commonly Used Discrete Distributions

Binomial Distribution Challenge: Solving Task Using Binomial Distribution Multinomial Distribution Geometric Distribution Poisson Distribution Challenge: Solving Task Using Poisson Distribution

4. Commonly Used Continuous Distributions

Continuous Uniform Distribution Exponential Distribution Challenge: Solving Task Using Exponential Distribution Gaussian Distribution Challenge: Solving Task Using Gaussian Distribution

5. Covariance and Correlation

What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

Challenge: Solving the Task Using Inclusion-Exclusion Principle

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 2. Capítulo 2

Challenge: Solving the Task Using Inclusion-Exclusion Principle

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 2. Capítulo 2

Challenge: Solving the Task Using Inclusion-Exclusion Principle

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Tarea

Let's imagine one situation that may be real for you. You have a tasty basket with:

5 cookies with a cherry jam,
5 chocolate cookies,
10 chocolate candies,
5 chocolate bars,
15 biscuits,
10 bottles of lemonade.

Calculate the probability that you will randomly pull out an item that includes chocolate, or a cookie.

We can divide our food into influential groups:

The first one: cookies (ones with cherry jam and chocolate).
The second one: is chocolate items (chocolate bars, candies, and chocolate cookies).

Follow the algorithm:

Calculate the probability of pulling out a cookie.
Calculate the probability of pulling out item that includes chocolate (chocolate sweet).
Calculate the probability of pulling out a chocolate cookie.
Calculate the resulting probability.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

Sección 2. Capítulo 2

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones