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Probability Theory Basics
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Probability Theory Basics

Probability Theory Basics

1. Basic Concepts of Probability Theory
Stochastic Experiment and Random EventProbability and It's PropertiesGeometrical ProbabilityChallenge: Solving the Task Using Geometric ProbabilityIndependence and Incompatibility of Random EventsConditional Probability
2. Probability of Complex Events
Inclusion-Exclusion PrincipleChallenge: Solving the Task Using Inclusion-Exclusion PrincipleThe Multiplication Rule of ProbabilityLaw of Total ProbabilityBayes' TheoremChallenge: Solving the Task Using Bayes' Theorem
3. Commonly Used Discrete Distributions
Binomial DistributionChallenge: Solving Task Using Binomial DistributionMultinomial DistributionGeometric DistributionPoisson DistributionChallenge: Solving Task Using Poisson Distribution
4. Commonly Used Continuous Distributions
Continuous Uniform DistributionExponential DistributionChallenge: Solving Task Using Exponential DistributionGaussian DistributionChallenge: Solving Task Using Gaussian Distribution
5. Covariance and Correlation
What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

bookChallenge: Solving the Task Using Inclusion-Exclusion Principle

Tarefa

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).

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.

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Tudo estava claro?

Como podemos melhorá-lo?

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Seção 2. Capítulo 2
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bookChallenge: Solving the Task Using Inclusion-Exclusion Principle

Tarefa

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).

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 desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
Tudo estava claro?

Como podemos melhorá-lo?

Obrigado pelo seu feedback!

Seção 2. Capítulo 2
toggle bottom row

bookChallenge: Solving the Task Using Inclusion-Exclusion Principle

Tarefa

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).

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 desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
Tudo estava claro?

Como podemos melhorá-lo?

Obrigado pelo seu feedback!

Tarefa

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).

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 desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
Seção 2. Capítulo 2
Switch to desktopMude para o desktop para praticar no mundo realContinue de onde você está usando uma das opções abaixo
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