Course Content

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

Task

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.

Task

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.

Everything was clear?

Section 2. Chapter 2

Challenge: Solving the Task Using Inclusion-Exclusion Principle

Task

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.

Task

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.

Everything was clear?

Section 2. Chapter 2

Challenge: Solving the Task Using Inclusion-Exclusion Principle

Task

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.

Task

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.

Everything was clear?

Task

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.

Section 2. Chapter 2

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