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Probability Theory Basics
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Kurssisisältö

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

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Challenge: Solving the Task Using Inclusion-Exclusion Principle

Tehtävä

Swipe to start coding

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.

Ratkaisu

Switch to desktopVaihda työpöytään todellista harjoitusta vartenJatka siitä, missä olet käyttämällä jotakin alla olevista vaihtoehdoista
Oliko kaikki selvää?

Miten voimme parantaa sitä?

Kiitos palautteestasi!

Osio 2. Luku 2
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book
Challenge: Solving the Task Using Inclusion-Exclusion Principle

Tehtävä

Swipe to start coding

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.

Ratkaisu

Switch to desktopVaihda työpöytään todellista harjoitusta vartenJatka siitä, missä olet käyttämällä jotakin alla olevista vaihtoehdoista
Oliko kaikki selvää?

Miten voimme parantaa sitä?

Kiitos palautteestasi!

Osio 2. Luku 2
Switch to desktopVaihda työpöytään todellista harjoitusta vartenJatka siitä, missä olet käyttämällä jotakin alla olevista vaihtoehdoista
Pahoittelemme, että jotain meni pieleen. Mitä tapahtui?
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