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Probability Theory
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Course Content

Probability Theory

Probability Theory

1. Learn Basic Rules
Random VariableBernoulli Trial 1/2Bernoulli Trial 2/2Binomial Probability 1/2Binomial probability 2/2
2. Probabilities of Several Events
Add ProbabilitiesCalculate Connected ProbabilitiesChallengeMultiply probabilitiesDependent probabilitiesLaw of Total ProbabilityBayes Theorem Challenge
3. Conducting Fascinating Experiments
The First ExperimentThe Second ExperimentThe Third ExperimentCombine Your Knowledge
4. Discrete Distributions
Discrete Uniform DistributionCalculate Fascinating ProbabilityBernoulli DistributionBinomial DistributionChallengePoisson DistributionChallenge
5. Normal Distribution
Normal DistributionChallenge 1Сhallenge 2

Challenge

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:

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

chocolate

Follow the algorithm:

  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.

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:

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

chocolate

Follow the algorithm:

  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.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 2. Chapter 3
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Challenge

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:

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

chocolate

Follow the algorithm:

  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.

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:

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

chocolate

Follow the algorithm:

  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.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 2. Chapter 3
toggle bottom row

Challenge

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:

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

chocolate

Follow the algorithm:

  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.

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:

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

chocolate

Follow the algorithm:

  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.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

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:

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

chocolate

Follow the algorithm:

  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.

Switch to desktop for real-world practiceContinue from where you are using one of the options below
Section 2. Chapter 3
Switch to desktop for real-world practiceContinue from where you are using one of the options below
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