Course Content

Probability Theory Basics

## Probability Theory Basics

# 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?

# 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.

**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?

# 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.

**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.

**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.

**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.