Challenge: Solving the Task Using Inclusion-Exclusion Principle | Probability of Complex Events
Probability Theory Basics

Course Content

Probability Theory Basics

Probability Theory Basics

1. Basic Concepts of Probability Theory
2. Probability of Complex Events
3. Commonly Used Discrete Distributions
4. Commonly Used Continuous Distributions
5. Covariance and Correlation

Challenge: Solving the Task Using Inclusion-Exclusion Principle

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:

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

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

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:

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

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

Everything was clear?

Section 2. Chapter 2

Challenge: Solving the Task Using Inclusion-Exclusion Principle

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:

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

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

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:

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

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

Everything was clear?

Section 2. Chapter 2

Challenge: Solving the Task Using Inclusion-Exclusion Principle

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:

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

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

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:

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

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

Everything was clear?

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:

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