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Probability Theory Basics
course content

Course Content

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 Bayes' Theorem

Task

Imagine that we decided to conduct medical research.
You gathered data about two groups: 750 people with heart problems and 800 with chronic stomachache.
You know that 7% of interviewed from the first group have diabetes; meanwhile, 12% of respondents from the second group have diabetes too.
Calculate the probability that a randomly selected person with diabetes has a chronic stomachache.

We can use Bayes' theorem to calculate the corresponding probability.

  1. Calculate the probability that a randomly selected person has a heart problem.
  2. Calculate the probability that the randomly selected person has a stomachache.
  3. Calculate the probability that you randomly select a person that has diabetes.

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Section 2. Chapter 6
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bookChallenge: Solving the Task Using Bayes' Theorem

Task

Imagine that we decided to conduct medical research.
You gathered data about two groups: 750 people with heart problems and 800 with chronic stomachache.
You know that 7% of interviewed from the first group have diabetes; meanwhile, 12% of respondents from the second group have diabetes too.
Calculate the probability that a randomly selected person with diabetes has a chronic stomachache.

We can use Bayes' theorem to calculate the corresponding probability.

  1. Calculate the probability that a randomly selected person has a heart problem.
  2. Calculate the probability that the randomly selected person has a stomachache.
  3. Calculate the probability that you randomly select a person that has diabetes.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Section 2. Chapter 6
toggle bottom row

bookChallenge: Solving the Task Using Bayes' Theorem

Task

Imagine that we decided to conduct medical research.
You gathered data about two groups: 750 people with heart problems and 800 with chronic stomachache.
You know that 7% of interviewed from the first group have diabetes; meanwhile, 12% of respondents from the second group have diabetes too.
Calculate the probability that a randomly selected person with diabetes has a chronic stomachache.

We can use Bayes' theorem to calculate the corresponding probability.

  1. Calculate the probability that a randomly selected person has a heart problem.
  2. Calculate the probability that the randomly selected person has a stomachache.
  3. Calculate the probability that you randomly select a person that has diabetes.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Everything was clear?

How can we improve it?

Thanks for your feedback!

Task

Imagine that we decided to conduct medical research.
You gathered data about two groups: 750 people with heart problems and 800 with chronic stomachache.
You know that 7% of interviewed from the first group have diabetes; meanwhile, 12% of respondents from the second group have diabetes too.
Calculate the probability that a randomly selected person with diabetes has a chronic stomachache.

We can use Bayes' theorem to calculate the corresponding probability.

  1. Calculate the probability that a randomly selected person has a heart problem.
  2. Calculate the probability that the randomly selected person has a stomachache.
  3. Calculate the probability that you randomly select a person that has diabetes.

Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
Section 2. Chapter 6
Switch to desktopSwitch to desktop for real-world practiceContinue from where you are using one of the options below
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