A virtual bag holds four distinguishable tokens: three blue and one gold. A draw gives every token the same chance. These rules let us calculate before simulating.
The four elementary outcomes are blue 1, blue 2, blue 3 and gold 1. “Blue” is an event containing three outcomes. With equal chances, P(blue) = 3/4 = 75%; P(gold) = 1/4 = 25%.
2
Do not count just the two colors as if they had equal chances. Counting favorable/possible outcomes works this way when elementary outcomes are equally likely. A physical bag may require checking whether its mechanism fits the model.
3
In this simulation, the token returns before each draw. The composition stays three out of four and the modeled draws are independent. A run of gold tokens does not create a debt requiring the next one to be blue.
4
Without replacement, after removing a blue token there are two blue among three tokens: the next chance changes to 2/3. State the rules before multiplying probabilities; do not assume independence just because there are two events.
Evidence lab
Experiment with fictional deliveries at Aurora station. Analysis runs in this browser. Nothing entered here is sent to the server.
The workshop resets when you leave or reload. Download data and report to keep your work, or send the report to the activity editor, which keeps a draft in this browser. Completion and XP belong to the account.
Header id,group,minutes; one delivery per row; unique id; groups A/B; decimal point; duration 0–1440 with up to two decimal places. Blank means unknown. Up to 100 rows. No quotes or decimal commas. Use invented data.
Selection uses the entered table, including missing values. A draw does not guarantee representativeness. The same seed reproduces selection; it cannot recover cases outside the table.
Make a prediction and analyze the table.
Selection results
Selection results
Group
Records
Known
Missing
Mean (min)
Median (min)
Range (min)
Within 5 min / known
Summaries rounded to up to two decimal places. Percentages use known durations; missing values remain outside that denominator. This does not remove possible missingness bias.
Individual durations (minutes)Bars begin at zero and show up to 20 known durations from the selection. The table below contains all selected records, including missing values.Inspect selected records
Inspect selected records
id
Group
Duration (min)
Virtual bag: model with replacement
There are four equally likely tokens; choose how many are blue. Each token returns before the next draw. This is a deterministic simulation, without prizes, money or real observations.
Repeating the seed repeats the sequence. More draws do not guarantee a closer result in every run and do not validate the real-world model.
Two rules, the same accuracy
Ten fictional cases: nine normal and one failure. Rules defined for this example; no AI training or real equipment testing. Same number correct, different consequences.
Two rules, the same accuracy
Rule
Correct / total
Missed failures
False alarms
Your investigation report
All recordsAnalyze selectionAlways normalBlue tokens out of four (0–4)Challenge: other routesData or selection changed. Analyze again before generating the report.Individual durations (minutes)Bars begin at zero and show up to 20 known durations from the selection. The table below contains all selected records, including missing values.Report sent to editor. Check and personalize it before saving or publishing.Correct / totalDownload input CSVInput data (simple CSV)Replace the current editor text with this report? Download any draft you want to keep first.Check the table or settings:Choose 0–4 blue tokens.Each row needs three comma-separated fields.Duplicate id. Check case identifiers.Include at least one record.Group must be A or B.Use header id,group,minutes.Id: 1–16 letters, digits, hyphens or underscores.Choose a valid selection method.Use at most 100 records.Sample size must be from 1 to the total number of records, without repeats.Seed must be an integer from 0 to 999999.Text must be at most 16000 characters.Choose 1–1000 draws.Use duration 0–1440, up to two decimal places with a dot, or leave blank.Example to investigateFalse alarmsFirst rowsHeader id,group,minutes; one delivery per row; unique id; groups A/B; decimal point; duration 0–1440 with up to two decimal places. Blank means unknown. Up to 100 rows. No quotes or decimal commas. Use invented data.GroupRecords in the input tableInterpretation and comparisonExperiment with fictional deliveries at Aurora station. Analysis runs in this browser. Nothing entered here is sent to the server.KnownLimitation, new scenario, help and reviewLineLoad exampleMean (min)Median (min)Record selectionDuration (min)Missed failuresMissingMissions: data and missingnessNo known dataObserved blue frequencyOpen index.html in a browser; all calculations work offline. Source links and your Rullst Academy account need a connection. The workshop does not automatically save edits: download CSV and report before closing.Analysis updated. Check units, missing values and limits.Within 5 min / knownOptional, if Node.js is already installed: run the tests below in the extracted folder. Node is not needed to use the workshop. Tests check calculations and technical limits, not student learning.Extreme valueQuestion, population, unit and predictionPseudorandom, without replacementRange (min)Make a prediction and analyze the table.Loading the example will replace the current table. Continue?Download Markdown reportThis report exceeds the editor limit. Download the complete report and prepare a shorter version to publish.Study report using fictional data. Selection and calculation do not establish causality, generalization or professional competence. The workshop does not verify human review; record it if pending.Your investigation reportSelection resultsSummaries rounded to up to two decimal places. Percentages use known durations; missing values remain outside that denominator. This does not remove possible missingness bias.Inspect selected recordsRuleTen fictional cases: nine normal and one failure. Rules defined for this example; no AI training or real equipment testing. Same number correct, different consequences.Two rules, the same accuracySample sizeThe workshop resets when you leave or reload. Download data and report to keep your work, or send the report to the activity editor, which keeps a draft in this browser. Completion and XP belong to the account.Second ruleSeed (0–999999)Selected idsSelection uses the entered table, including missing values. A draw does not guarantee representativeness. The same seed reproduces selection; it cannot recover cases outside the table.Settings changed; run the simulation to update.Repeating the seed repeats the sequence. More draws do not guarantee a closer result in every run and do not validate the real-world model.There are four equally likely tokens; choose how many are blue. Each token returns before the next draw. This is a deterministic simulation, without prizes, money or real observations.Virtual bag: model with replacementSimulate and compareSame mean, different distributionTheoretical probabilityEvidence labSend report to editorRecordsDraws (1–1000)Not filled in yetUnknown# My investigation
## Before calculating
- Question, population, unit and prediction:
- Fictional data, source and selection method:
## Check and compare
- Missing data, duplicates and recorded decisions:
- Manual calculation and workshop check:
- Center, spread, proportion and representation:
- Original variation and a case that changes my conclusion:
## Interpret and review
- What the data supports:
- What it does not yet support:
- Simple baseline comparison, when relevant:
- Feedback received or external review pending:
- Help from people/AI and my own checks:
- After a break, another table and explanation without copying:
Download CSV and report. The editor draft is not an automatic copy of the workshop. GitHub is optional; do not publish personal data.
Draw five tokens, two blue. Calculate the initial chance and the blue chance after removing one blue without replacement. Explain why they differ without needing a real draw.
At your own pace
My files and GitHub
Every lesson can become your own record: code, notes or a practice plan. Saving a file to GitHub is optional and does not change your XP.
Download the lesson example and a workbook for your notes. The ZIP includes a guide to organizing activities in one or more repositories. Publishing is optional; eligible accounts can also use the GitHub upload button.
Your file for this lesson
Edit the example or record what you learned. This space does not run code or grade answers. The draft is saved only in this browser, separately per account; you choose when to download or upload to GitHub.
The example may be only a snippet or outline. Changing the extension does not make it a complete program. The activity ZIP contains starting material; the edited-file button downloads your text.
Your text will be saved in this browser when you edit it. On a shared computer, clear your drafts when finished.
As a visitor, this draft belongs to the browser and will not transfer to an account. Download a copy before signing in or creating an account.
Direct upload accepts up to 8 KiB of text in one file. Use downloads and the manual guide for projects with multiple files.
Save to my GitHub
Choose an authorized personal repository. Each upload creates a new file in an activity folder; existing content is preserved. You decide whether to use one repository or different destinations.
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A question, a little curiosity and the courage to try are enough. Every small step counts here, including the ones you take again. Learn at your own pace, celebrate your discoveries and bring your imagination to life.Choose a nickname in your user profile whenever you like. Your profile starts private; sharing achievements and joining the ranking are your choices.A space that feels like youConfirm your email before signing in. If the address is eligible for registration, you’ll receive a link. Check your spam folder too. Already have an account? Sign in or request a password reset.Read the welcome againWith care, Rullst. Let’s create together.WelcomeYour nickname and profileYour space for discoveryAnswers drafted in this browser. Only a confirmed completion records progress.Back to the catalogChoose an available card to begin. Each track has its own page and lesson sequence.Track achievementYou completed every activity in this track. 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Download a copy before signing in or creating an account.Download the track’s final projectAvailable after completing the track. The ZIP contains the project files; your edits in this space remain in the edited file.Direct upload accepts up to 8 KiB of text in one file. Use downloads and the manual guide for projects with multiple files.The example may be only a snippet or outline. Changing the extension does not make it a complete program. The activity ZIP contains starting material; the edited-file button downloads your text.What I understood:
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How I checked the result:
A question or next step:
My learning recordThe quiz ZIP uses the last creation completed and saved to your account. Unchecked form changes or edits in this editor do not change that ZIP.Choose a scenarioMini experimentLearning simulation: compare cards and check your predictions. The browser is not compiling Rust or starting a server.This scenario’s resultShow resultYour guardian needs to enable this track in My account. Existing achievements remain saved.Other tracks the learner may practiceNew tracks start disabled. The general pause applies to all. Limits control account activities and progress; public text remains accessible.Rullst quiz: last permitted lesson (1 to 8)Try the first lesson of each track. Sign in or create an account to save progress and continue.From first discoveries to advanced projects. Explore mathematics, programming and new ideas with Rust and Rullst. Learn, experiment and create at your own pace.Your snippet in progressanswers preparedBuild your answers and check when you are ready.Discovery workshopMove cards with the arrows and check your sequence.lessonsFor curious people, even without prior interest in programming. Observe, compare and explain decisions using fictional situations.Investigative mindInvestigate claims, plan fair tests and check sources. Finish by assembling your own investigation.Download investigation workbookAn editable Markdown guide for applying questions, tests, records and revision outside Rullst Academy. Use safe situations and fictional data.Separate observation, preference and hypothesis.Plan tests and check the limits of evidence.Build a workbook for your own investigation.Idea detective22 lessons availableChoose a track and move at your own pace. Each has its own sequence, practice and achievement; you do not need to finish another track before starting.Direct uploads require an adult account with confirmed email and linked GitHub. Downloads remain available according to activity access.Choose a destination and check its path and visibility before confirming.I reviewed the code, destination and visibility. I want to upload this file.GitHub denied access or requested a pause. Check permissions and try again later.Destination repositoryDownload my edited fileDownload started. Check your downloads folder; GitHub upload is separate.Edit the example or record what you learned. This space does not run code or grade answers. The draft is saved only in this browser, separately per account; you choose when to download or upload to GitHub.The file already exists or the branch rejected the upload. Check the repository; nothing was overwritten. For a new version, edit the text and review again.Choose an authorized personal repository. 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Create one with a README and select it in the installation, or load the next page when available.One repository for all activitiesOpen my file on GitHubHow I want to organizeIf you authorize activity uploads, the GitHub App accesses only repositories selected during installation. The Rullst Academy checks the linked GitHub ID, its installation and the repository list to validate the destination. After your confirmation, it sends the reviewed text to a new file in the selected repository. The text and installation tokens are not stored in the Rullst Academy database. Destination preferences stay in this browser, separately per account, and can be removed with Clear local data. Deleting a Rullst Academy account does not delete files on GitHub; manage files and revoke the installation on GitHub itself. The editor draft also stays in this browser, separately per account and lesson. It does not follow you to another device; download a copy and clear drafts on shared computers.PrivatePublic: anyone can view itFile saved to GitHub. Open the link to inspect your commit.Upload file to GitHubUse up to 8 KB of text per upload. For larger projects, download the materials and upload manually.My code or notesSave to my GitHubDirect uploads are not available yet. You can download your file and follow the manual publishing guide.The repository visibility changed. Load it again and review before uploading.Your file for this lessonReview this trackFor anyone who wants to understand how a page works, starting from zero. Activities use small examples; reading the full code can come later.Idea gardener with RullstFollow a visit between browser and server, discover HTML and connect two pages. Then take your idea garden to your computer.Download my Rullst gardenA two-page Rullst 12 project, translated README and tests. Install Rust to run locally; the initial setup downloads dependencies.Understand the roles of Rust, Rullst and the browser.Connect routes, HTML structure and clear links.Check two pages, inserted text and a 404 error.Rullst: a page comes aliveFor anyone starting with clicks and their own quiz. No programming experience needed. To meet the tools first, try the introductory Rullst track.Turn a question into an interactive quiz.Experiment with answers, decisions and scoring.Take home a Rullst project with your quiz choices.For anyone who has never programmed or wants a gentle fresh start. No installation needed for the lessons. A trusted person can help with reading.First sparks in RustLight up a terminal, discover what quotes change and turn errors into clues. Your final mission: an explorer card built in Rust.Download my first Rust projectA terminal explorer card with instructions in your language. No external dependencies; requires Rust installed to run on your computer.Distinguish code, text and terminal output.Read names and calculations, using errors as clues.Prepare a Cargo project and check two cases.Rust: first sparksFor anyone wanting to practice code in small steps. This track introduces syntax; if everything still feels new, start with Rust: first sparks.Rust program builderValues, decisions, loops, functions, borrowing and Option. Build a scoring station and take home a runnable Rust project.Download Rust projectA Rust terminal program, without a framework. Includes comments in your language, a README and tests. The first track’s quiz project uses Rullst 12.Read values, conditions, loops and functions.Experiment with borrowing and absence using Option.Build and test a scoring station.Rust: from idea to programStart this trackTry the first lesson without an account. Sign in to save your achievements.Is this track for you?Your path, step by stepWhat you will discoverThe time is an estimate, not a deadline. Take breaks, use hints and try again whenever you need.There is still something to investigate. Use the hint and try again.Lesson completed and progress saved to your account.You changed the answer. Check again to validate this version.My files and GitHubChecking your access to this lesson…The editor and downloads open when this lesson is available to your account. Check access below or return to the track map.Every lesson can become your own record: code, notes or a practice plan. Saving a file to GitHub is optional and does not change your XP.Ready to check your answer.Read the feedback before trying again.Your tracksOne world, five territoriesDiscovery, Foundations, Building, Specialization and Frontiers represent depth. You advance through learning, with the support you need.Track completedChoose your route and learning space. Explore free tracks with reading support, three visual styles and saved progress.In the Aurora Expedition, we face the dragons of problems and ignorance with questions, knowledge and creativity. Mistakes give us clues for the next attempt.Dragons are the challenges.Explore this trackFind a starting point and choose the setting for your journey.What will you discover next?With JavaScript disabled, all suggestions appear below. Track links remain available.My routeI prefer to explore allExplore • imagine • discoverAsk • experiment • testBuild • understand • go deeper{done} of {total} lessonsProgress has not loaded yet. You can still explore the tracks.Reading supportIn lessons, Listen uses voices available on your device. You can also share reading with someone.Suggestions to exploreRemember choices in this browserNo completed lessons at this stop.Your spaceChoices apply on this page only.Reference stageThis choice recommends content. It does not report or change account age or grant permissions.The preference could not be saved. Your choice applies on this page; check browser storage permissions.Changing routes preserves your achievements. You can return here whenever you like.Current space: Adventure — rounded shapes, illustrations and gentle motion.Current space: Laboratory — a grid background, technical details and moderately rounded shapes.Current space: Studio — straighter lines, a clean background and less decorative motion.Space updated. Your achievements stay with you.Choices reset. Explore at your own pace.Your choices stay in this browser. They do not change your account or family permissions.Sign in to keep achievements. You can try the first lesson of each track without an account.18+ · Develop skillsAges 15–17 · Build my futureAges 5–7 · Discover through playAges 12–14 · Try different pathsAges 8–11 · Create and investigateIn upcoming advanced work, we will practice clear requirements, reviewing suggested code, failure tests and explained decisions. Learning to use AI includes knowing how to check the result.Learn with AI, check with evidenceAll possibilitiesShow suggestionsStudy available foundationsAll learning programsDiscover what people create at workA career path combines foundations, work tasks, projects and assessment. Today you can study the published foundations and explore the full plan.Careers in the age of AICareer pathsExplore careersConnect skills to professional tasks, original projects and practical assessment. Roadmaps show available stages and what is still needed.How would you like to explore?Choose a skill, explore a career or discover upcoming specializations. See what you can already study at Rullst Academy.Explore learning programsA discovery can become a projectA first experience for youIn preparationSign in to see the progress you have already earned.Develop skills through your own projectsBuild projects for your futureShall we discover what we can create?Try a field and find your pathYour ideas can come to lifeExplore development, security, AI, data and cloud. Each path shows what you can study now and what we are preparing.From your first ideas to professional projectsYour knowledge may go beyond the suggestion. Adventure, Laboratory and Studio styles remain independent.Start from scratch, build on what you have studied or deepen your knowledge. The roadmap shows available foundations and upcoming professional preparation.Connect foundations, original projects and professional skills. Develop autonomy gradually, with support in activities that need guidance.With an adult, choose a discovery. Observe, play and explain by pointing or drawing. The first activities need shared reading.Discover different fields through projects and see the full roadmap. Experiment before choosing where to go deeper.Try creating, investigating and caring for the digital world. Discover professions through small projects, with support when you need it.Your progress has not loaded yet.Editorial review: 2026-09-26. Source: a 2025 global employer survey; not a country- or language-specific job listing analysis or a hiring promise.Read the WEF reportSoftware, AI and data, networks and cybersecurity feature in the WEF skills and jobs growth outlook for 2030. Our first career path builds on the Rust and Rullst foundations already published.Why learn these skills?Other planned specializations: AI application security and Rust performance. Each path will have its own prerequisites, projects and assessment criteria.Learning programsFoundations available · career path in developmentView the roadmapPlanned · lessons not yet availablePost-quantum cryptographyA future security specialization: study quantum-resistant cryptography, inventory and migration. These algorithms can run on ordinary computers; this differs from programming quantum circuits.Explore the professional goal too{done} of {total} lessons completedThis shows progress in available tracks. Completing these foundations does not complete milestones in preparation or award professional certification.The project we want to help you buildGoal of the complete career path, still in preparation. You can start with the published foundations and build at your own pace.Quantum computingStart with the available mathematics and probability foundations. The quantum path is still being planned.Explore mathematics foundationsAn initial discovery of bits, qubits and measurement, followed by mathematical foundations and small simulated circuits. Advanced study will cover algorithms, noise and limitations.Your learning roadmapThe tracks below are available to study. Each milestone also shows the deeper work still needed to complete the career path.Your progress in published foundationsSkill pathsExplore skillsLearn a skill such as Rust, SQL, Git or critical thinking. Use these foundations across different careers.SpecializationsSee upcoming specializationsGo deeper into a subject after building the required foundations. The new paths below are being planned.Choose a reference for suggestions. It does not declare your age or change account permissions.Start with this discoveryAdjust my journey and styleWhat would you like to learn to build?Different ways to learnChoose an option and use colors in #RRGGBB format.CardsYour adventure starts with youChoose your characterChoose your character to begin1. Choose a class and an appearance2. Give your adventure its colorsEvery class can explore every track. This is a visual choice: it changes neither XP nor difficulty. Outfits and equipment are fixed. Your character does not need to resemble you.CompletedA colossal dark-scaled dragon with biomechanical wings, AI sensors and laser emitters above a citadel in the clouds.Defeat the dragons of ignorance and problems.Investigate a question, test an idea and solve a challenge. Each discovery opens a new path.Customize characterExplore the world mapEye colorOpen eye color pickerFaceFace 1 · European inspirationFace 2 · Asian inspirationFace 3 · African inspirationHair colorChoose hair colorUse the picker or type # followed by six characters from 0–9 or A–F. Example: #AF795B. Imaginary colors are welcome too!In progressOne editor, two styles to explore. Choose your character, customize and save when ready.Customize your characterChildren's adventureCloseChoose a children's adventure characterEnlarge portraitLittle explorerYoung explorerBrown-skinned girl with a long braid and orange backpack, holding a notebook and magnifying glass beside a geometric leaf.Magnifying glass in hand, questions in a notebook. The world has clues waiting for you.Does one leaf look like another? The explorer observes, sketches and compares before deciding. Every good question opens a new path.Observe · ask · discoverEast Asian boy with black hair, an orange backpack, a magnifying glass and an open notebook in a futuristic garden.Magnifying glass in hand, questions in a notebook. The world has clues waiting for you.He found an unusual seed in the garden. Before deciding what it is, he observes its shape, sketches it and compares it with others. A good question can open up a great adventure.Observe · ask · discoverFeminineChoose a face and customize skin, eyes and hair. Original colors are always available.Little guardianYoung guardianBlack girl with short coiled hair and an orange scarf, holding a small glowing bridge model.Courage also means asking for help, welcoming someone and finding a solution together.A bridge should work for the people crossing it. The guardian listens to the group, tests paths and helps everyone take part in the discovery.Care · collaborate · connectBrown-skinned child with wavy hair, a hearing aid and a green jacket, offering a hand and holding a small glowing bridge.Courage also means asking for help, welcoming someone and finding a solution together.The crew wants to cross a stream. He invites everyone to draw a bridge and tests a small model with his friends. Each person contributes in their own way. Together, they find a safe path.Care · collaborate · connectChoose a character, try its appearances and colors, and save your choice.Little inventorYoung inventorBoy with curly auburn hair and glasses, using a wheelchair and holding a robot crab on his lap.An idea, a few parts and lots of curiosity. Every attempt reveals something new!A wheel and a claw can respond to commands. Our inventor tests one change at a time and explains his discoveries so everyone can build together.Imagine · build · tryBlack girl with curly hair, safety goggles on her forehead and a light jacket, holding an orange and green robot crab.An idea, a few parts and lots of curiosity. Every attempt reveals something new!She built a robot crab to explore the garden. When it heads the wrong way, they observe, change one part and try again. Learning also means discovering what can still be improved.Imagine · build · tryMasculineYour character joins you in your account and on the map. Appearance does not change your lessons or permissions.Original colorsPresentationChoose this characterMeet the characterLittle heroes, big discoveriesMagicMage · feminineMage · masculineImagine what does not exist yetAdventure mapTravel through gardens, workshops and cities of the future. Each stop is a real Rullst Academy track. Choose a region or use the filters to find your next mission.The path suggests an order, not an obligation. Setup tracks for different systems are alternatives. Planned regions do not have available lessons yet.A world to discover. One step at a time.To exploreMagic, science and courage meet to discover technology. Choose your character and join our robot crab across islands of knowledge — from your first ideas to new worlds.Every great adventure begins with a choice.Character previewYour character is saved to your account. It appears on your public profile only if you enable that option in profile settings.{done} of {total} lessons completedCity of MakersGardens of DiscoveryIdea WorkshopsStellar HorizonsCitadel of KnowledgeRegions of knowledgeDiscard changesChanges discarded. Your saved character was preserved.This account is restricted. Changes are unavailable.Save my characterCharacter saved to your account. The adventure continues!Saving character…ScienceScientist · feminineScientist · masculineTurn questions into discoveriesTry the options. Sign in to save your character.Skin colorOpen skin color pickerLittle Inventors: child characters. Aura Masters: teen and adult characters. Explore the styles and save your favorite.Character stylesSwitch appearanceUse the arrow to switch between feminine and masculine, and the Face menu to explore each class's portraits. You can change your hero and colors whenever you like.Aura MastersLittle InventorsPreview updated. Save to keep it in your account.Track presentationChecking your account…WarriorWarrior · feminineWarrior · masculineMeet challenges with creativityHere, curiosity becomes discovery and every attempt helps you grow. Our robot crab has prepared the path. Choose who will accompany your journey, at your pace and in your colors.Rullst universe · Aurora expeditionYour journey companion
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Rullst Academy