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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 Task Using Binomial Distribution

Let's consider a task about shooting at a target.
The probability of hitting the target in a single shot is 0.6. We want to calculate the probability of hitting the target 4 times in 10 shots.

We can't solve this task using the classic definition of probability because elementary events of this stochastic experiment have different probabilities of occurring. In addition, we are conducting not one stochastic experiment but ten, and we need to consider the results of all individual experiments.
This stochastic experiment is a Bernoulli trial: we have only two possible outcomes ( shoot and fail to shoot the target).
Shots are independent, so we have a Bernoulli process and can calculate probability using Binomial distribution.

Task

You have to calculate the probability of hitting the target 4 times in 10 shots.

Use .pmf() method and specify n and p parameters to calculate the corresponding probability.

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Section 3. Chapter 2
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bookChallenge: Solving Task Using Binomial Distribution

Let's consider a task about shooting at a target.
The probability of hitting the target in a single shot is 0.6. We want to calculate the probability of hitting the target 4 times in 10 shots.

We can't solve this task using the classic definition of probability because elementary events of this stochastic experiment have different probabilities of occurring. In addition, we are conducting not one stochastic experiment but ten, and we need to consider the results of all individual experiments.
This stochastic experiment is a Bernoulli trial: we have only two possible outcomes ( shoot and fail to shoot the target).
Shots are independent, so we have a Bernoulli process and can calculate probability using Binomial distribution.

Task

You have to calculate the probability of hitting the target 4 times in 10 shots.

Use .pmf() method and specify n and p parameters to calculate the corresponding probability.

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 3. Chapter 2
toggle bottom row

bookChallenge: Solving Task Using Binomial Distribution

Let's consider a task about shooting at a target.
The probability of hitting the target in a single shot is 0.6. We want to calculate the probability of hitting the target 4 times in 10 shots.

We can't solve this task using the classic definition of probability because elementary events of this stochastic experiment have different probabilities of occurring. In addition, we are conducting not one stochastic experiment but ten, and we need to consider the results of all individual experiments.
This stochastic experiment is a Bernoulli trial: we have only two possible outcomes ( shoot and fail to shoot the target).
Shots are independent, so we have a Bernoulli process and can calculate probability using Binomial distribution.

Task

You have to calculate the probability of hitting the target 4 times in 10 shots.

Use .pmf() method and specify n and p parameters to calculate the corresponding probability.

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!

Let's consider a task about shooting at a target.
The probability of hitting the target in a single shot is 0.6. We want to calculate the probability of hitting the target 4 times in 10 shots.

We can't solve this task using the classic definition of probability because elementary events of this stochastic experiment have different probabilities of occurring. In addition, we are conducting not one stochastic experiment but ten, and we need to consider the results of all individual experiments.
This stochastic experiment is a Bernoulli trial: we have only two possible outcomes ( shoot and fail to shoot the target).
Shots are independent, so we have a Bernoulli process and can calculate probability using Binomial distribution.

Task

You have to calculate the probability of hitting the target 4 times in 10 shots.

Use .pmf() method and specify n and p parameters to calculate the corresponding probability.

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