{"version":3,"file":"P009-pVONBrSA.js","sources":["../../src/exercices/profs/P009.js"],"sourcesContent":["import { repere } from '../../lib/2d/reperes.js'\nimport { traceBarre } from '../../lib/2d/diagrammes.js'\nimport { nombreAvecEspace, texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint, calculANePlusJamaisUtiliser } from '../../modules/outils.js'\nimport { fraction } from '../../modules/fractions.js'\n\nexport const titre = 'Simulation of random experiments'\nexport const ref = 'P009'\nexport const uuid = '691a7'\n\n/**\n * Reconnaître une fonction affine\n* @author Erwan Duplessy\n* 6C30-1\n* D'après le document \"Attendus en fin de 3eme\"\n* On donne les fréquences d\\'apparition de chaque face d\\'un dé pour 10000 lancers.\n* L\\'élève interprète les résultats en les comparant aux probabilités théoriques.\n*/\n\nexport default function SimulateurAleatoire () {\n  Exercice.call(this)\n  this.nbQuestions = 1 // Ici le nombre de questions\n  this.nbQuestionsModifiable = true // Active le formulaire nombre de questions\n  this.nbCols = 1 // Le nombre de colonnes dans l'énoncé LaTeX\n  this.nbColsCorr = 1// Le nombre de colonne pour la correction LaTeX\n  // See the Exercise Class for an exhaustive list of available properties.\n  this.correctionDetailleeDisponible = true\n  this.correctionDetaillee = true\n  this.sup = 1 // situation 1=dés\n  this.sup2 = 10000 // nbLancers\n  this.sup3 = false // true = équiprobable, false = jeu truqué\n\n  // this.consigne = '<center><a title=\"Diacritica, CC BY-SA 3.0 &lt;https://creativecommons.org/licenses/by-sa/3.0&gt;, via Wikimedia Commons\" href=\"https ://commons.wikimedia.org/wiki/File:Dice_(typical_role_playing_game_dice).jpg\"><img width=\"128\" alt=\"Dice (typical role playing game dice)\" src=\"https://upload.wikimedia .org/wikipedia/commons/thumb/e/e5/Dice_%28typical_role_playing_game_dice%29.jpg/128px-Dice_%28typical_role_playing_game_dice%29.jpg\"></a></center>'\n\n  // this is where the exercise code begins this function creates a copy of the exercise\n  this.nouvelleVersion = function () {\n    // the numeroExercice variable can be retrieved to allow two copies of the same exo to be differentiated\n    // For example, to be sure not to have the same point names by calling this exo twice on the same page\n\n    let texte = '' // Nous utilisons souvent cette variable pour construire le texte de la question.\n    let texteCorr = ''\n    let nbFaces = 2 * randint(1, 5) + 2 // nombre de faces du dé : 4, 6, 8, 10 ou 12\n    const nbLancers = parseInt(this.sup2) // nombre de lancers\n    const tabEff = []// tableau d'effectifs temporaires - une dimension [eff]\n    let S = 0 // effectif total\n    const tabRes = [] // tableau des fréqeunces observées - deux dimensions [val, freq]\n    this.listeCorrections = []\n    this.listeQuestions = []\n    const tabcoul = ['red', 'green', 'blue', 'black']\n    const tabNbBoules = [randint(2, 5), randint(2, 5), randint(2, 5), randint(2, 5)]\n    let nbBoules = 0; let f; let choix\n    let face\n    for (let i = 0; i < 4; i++) {\n      nbBoules += tabNbBoules[i]\n    }\n\n    switch (parseInt(this.sup)) { //\n      case 1: // Tirages de dés\n        f = fraction(1, nbFaces)\n        texteCorr = `Each face has the same probability of coming out: $${f.texFraction}\\\\approx ${texNombre(f.pourcentage, 2)}\\\\%$.<br>`\n\n        texte += `We roll a die with ${nbFaces} faces ${nombreAvecEspace(nbLancers)} times.<br>We study the frequencies of appearance of each face.<br>We obtain the following results: <br>`\n        if (this.sup3) {\n          for (let i = 0; i < nbFaces; i++) {\n            tabEff.push(0)\n          }\n          for (let i = 0; i < nbLancers; i++) {\n            tabEff[randint(1, nbFaces) - 1]++\n          }\n          for (let i = 0; i < nbFaces; i++) {\n            tabRes[i] = [i, calculANePlusJamaisUtiliser(tabEff[i] / nbLancers)]\n          }\n        } else {\n          face = randint(1, nbFaces) // on choisit une face au hasard. Elle aura une fréquence déséquilibrée.\n          for (let i = 0; i < nbFaces; i++) {\n            tabEff.push(0)\n          }\n          for (let i = 0; i < nbFaces; i++) {\n            tabEff.push(0)\n          }\n          for (let i = 0; i < nbLancers; i++) {\n            tabEff[randint(1, nbFaces) - 1]++\n          }\n          S = tabEff[face - 1] * 3 / 4\n          tabEff[randint(1, nbFaces, face) - 1] += S\n          tabEff[face - 1] -= S\n          for (let i = 0; i < nbFaces; i++) {\n            tabRes[i] = [i, calculANePlusJamaisUtiliser(tabEff[i] / nbLancers)]\n          }\n          texteCorr += 'Here, experience shows that there is something which seems to distort this equiprobability like a rigged die.<br>'\n          texteCorr += `Indeed, the frequency of the face $${face}$ is much lower than $${texNombre(f.pourcentage, 2)}\\\\%$.`\n        }\n\n        break\n\n      case 2: // Tirage dans une urne\n        face = randint(1, 4)\n        texte += 'Balls of different colors are placed in an urn.<br>'\n        texte += `There are $${tabNbBoules[0]}$ ${tabcoul[0]}, $${tabNbBoules[1]}$ ${tabcoul[1]}, $${tabNbBoules[2]}$ ${tabcoul[2]} and $${tabNbBoules[3]}$ ${tabcoul[3]}.<br>`\n        texte += `We carry out $${texNombre(nbLancers)}$ draws with discount.<br>`\n        texte += 'We study the frequencies of appearance of each color.<br>We obtain the following results: <br>'\n        f = fraction(tabNbBoules[face - 1], nbBoules)\n        if (this.sup3) {\n          nbFaces = 4\n          for (let i = 0; i < nbFaces; i++) {\n            tabEff.push(0)\n          }\n          for (let i = 0; i < nbLancers; i++) {\n            choix = randint(1, nbBoules)\n            if (choix <= tabNbBoules[0]) {\n              tabEff[0]++\n            } else if (choix <= tabNbBoules[0] + tabNbBoules[1]) {\n              tabEff[1]++\n            } else if (choix <= tabNbBoules[0] + tabNbBoules[1] + tabNbBoules[2]) {\n              tabEff[2]++\n            } else {\n              tabEff[3]++\n            }\n          }\n          for (let i = 0; i < nbFaces; i++) {\n            tabRes[i] = [i, calculANePlusJamaisUtiliser(tabEff[i] / nbLancers)]\n          }\n        } else {\n          nbFaces = 4\n          for (let i = 0; i < nbFaces; i++) {\n            tabEff.push(0)\n          }\n          for (let i = 0; i < nbLancers; i++) {\n            choix = randint(0, nbBoules - 1)\n            if (choix < tabNbBoules[0]) {\n              tabEff[0]++\n            } else if (choix < tabNbBoules[0] + tabNbBoules[1]) {\n              tabEff[1]++\n            } else if (choix < tabNbBoules[0] + tabNbBoules[1] + tabNbBoules[2]) {\n              tabEff[2]++\n            } else {\n              tabEff[3]++\n            }\n          }\n          S = tabEff[face - 1] * 3 / 4\n          tabEff[randint(1, 4, face) - 1] += S\n          tabEff[face - 1] -= S\n          for (let i = 0; i < nbFaces; i++) {\n            tabRes[i] = [i, calculANePlusJamaisUtiliser(tabEff[i] / nbLancers)]\n          }\n          texteCorr += 'Here, experience shows that there is something that seems to distort this equiprobability like balls discernible by touch.<br>'\n          texteCorr += `Indeed, the frequency of ${tabcoul[face - 1]} balls is much lower than $${f.texFraction}\\\\approx ${texNombre(f.pourcentage, 2)}\\\\%$.`\n        }\n        break\n    }\n    switch (parseInt(this.sup)) {\n      case 1:\n        texte += '$\\\\begin{array}{|l|' + 'c|'.repeat(nbFaces) + '}\\not'\n        texte += '\\\\hline\\n'\n        texte += '\\\\text{Side number}'\n        for (let i = 0; i < nbFaces; i++) {\n          texte += ` & \\\\textbf{\\\\text{${i + 1}}}`\n        }\n        texte += '\\\\\\\\\\\\hline\\n'\n        texte += '\\\\text{Appearance frequency}'\n        for (let i = 0; i < nbFaces; i++) {\n          texte += ` & ${texNombre(100 * tabRes[i][1], 1)} \\\\%`\n        }\n        texte += '\\\\\\\\\\\\hline\\n'\n        texte += '\\\\end{array}\\n$'\n        texte += '<br>'\n        if (this.correctionDetaillee) {\n          const coef = 10\n          const r = repere({\n            grilleX: false,\n            grilleY: 'dots',\n            xThickListe: false,\n            xLabelListe: false,\n            yUnite: 1 / coef,\n            yThickDistance: 1 * coef,\n            yMax: 40,\n            xMin: 0,\n            xMax: 10,\n            yMin: 0,\n            axeXStyle: '',\n            yLegende: 'frequencies in %'\n          })\n\n          const lstElementGraph = []\n          for (let i = 0; i < nbFaces; i++) {\n          // lstElementGraph.push(traceBar(((r.xMax - r.xMin) / nbFaces) * (i + 0.5), tabRes[i][1] * 10, i + 1), { unit: 1 / coef } )\n            lstElementGraph.push(traceBarre(((r.xMax - r.xMin) / nbFaces) * (i + 0.5), tabRes[i][1] * 10, i + 1))\n          }\n          texte += mathalea2d({ xmin: -1, xmax: 11, ymin: -4, ymax: 5.5, pixelsParCm: 30, scale: 1 }, r, lstElementGraph)\n        }\n        break\n      case 2:\n        texte += '$\\\\begin{array}{|l|' + 'c|'.repeat(nbFaces) + '}\\not'\n        texte += '\\\\hline\\n'\n        texte += '\\\\text{Color of the ball}'\n        for (let i = 0; i < nbFaces; i++) {\n          texte += ` & \\\\textbf{\\\\text{${tabcoul[i].substring(0, tabcoul[i].length - 1)}}}`\n        }\n        texte += '\\\\\\\\\\\\hline\\n'\n        texte += '\\\\text{Appearance frequency}'\n        for (let i = 0; i < nbFaces; i++) {\n          texte += ` & ${texNombre(100 * tabRes[i][1], 1)} \\\\%`\n        }\n        texte += '\\\\\\\\\\\\hline\\n'\n        texte += '\\\\end{array}\\n$'\n        texte += '<br>'\n        if (this.correctionDetaillee) {\n          const coef = 10\n          const r = repere({\n            grilleX: false,\n            grilleY: 'dots',\n            xThickListe: false,\n            xLabelListe: false,\n            yUnite: 1 / coef,\n            yThickDistance: 1 * coef,\n            yMax: 55,\n            xMin: 0,\n            xMax: 10,\n            yMin: 0,\n            axeXStyle: '',\n            yLegende: 'frequencies in %'\n          })\n\n          const lstElementGraph = []\n          for (let i = 0; i < nbFaces; i++) {\n            // lstElementGraph.push(traceBar(((r.xMax - r.xMin) / nbFaces) * (i + 0.5), tabRes[i][1] * 10, tabcoul[i]), { unit: 1 / coef })\n            lstElementGraph.push(traceBarre(((r.xMax - r.xMin) / nbFaces) * (i + 0.5), tabRes[i][1] * 10, tabcoul[i]))\n          }\n          texte += mathalea2d({ xmin: -1, xmax: 12, ymin: -4, ymax: 7, pixelsParCm: 30, scale: 1 }, r, lstElementGraph)\n        }\n        break\n    }\n\n    this.listeQuestions.push(texte)\n    this.listeCorrections.push(texteCorr)\n    listeQuestionsToContenu(this) // On envoie l'exercice à la fonction de mise en page\n  }\n  // If the following variables are defined, they cause the corresponding parameter forms to be displayed\n  // They can be of 3 types: _numeric, _checkbox_or _text.\n  // They are associated respectively with the sup, sup2 and sup3 parameters.\n\n  this.besoinFormulaireNumerique = ['Type of experience', 2, '1: Drawing of dice\\n 2: Drawing from an urn']\n  this.besoinFormulaire2Texte = ['Number of prints', `Type an integer: ${10000} for example`]\n  this.besoinFormulaire3CaseACocher = ['Equiprobability', true]\n} // Fin de 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