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概率模型在饼干配料中的应用

概率模型在饼干配料中的应用
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2023-07-27 23:33
概率统计函数图像
本范例通过条形图展示饼干配料频率数据，帮助学生理解概率与频率的关系。核心数学概念包括概率模型、频率统计和数据可视化。作图要点涉及使用GeoGebra命令如BarChart、RandomUniform等构建图表。适合6-8年级学生用于概率统计教学。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.9064980580961615, 0.7883330799764553, 0.19128575540605944, 0.2240338805383391, 0.17447995660816482, 0.052772053381752754, 0.7139692515865531, 0.628335415443585, 0.5976098983988584, 0.857802428704047, 0.19412731009430323, 0.14582161084410622, 0.18179862805624677, 0.7569167562869002, 0.04036425567121437, 0.1293707809881714, 0.9289142864231259, 0.4240521136825159, 0.18977913243407443, 0.350694411678108, 0.014383043926408002, 0.4371435882810758, 0.12135215799583529, 0.8733120471630028, 0.018253376195172807, 0.42273646525394587, 0.6406207044659178, 0.21227553272729954, 0.5734397433387318, 0.7235050734477635, 0.18013681399705883, 0.3515090139878073, 0.0600857835235189, 0.44410960897056995, 0.781516380016482, 0.9330589967982462, 0.9198990328486611, 0.12159486084190897, 0.11089619177493337, 0.43816358861013543, 0.5289093745821424, 0.8744927401730133, 0.2603082527522874, 0.6678531746057637, 0.9513897182643934, 0.149937492929613, 0.8328615558332118, 0.610784798944692, 0.17165304373469448, 0.28043631734685354, 0.49969033158383397, 0.5181903966915694, 0.8741007566817723, 0.6814597989073239, 0.9413829544190095, 0.8601840620689782, 0.44524852787651836, 0.02772514481738545, 0.7260496585586066, 0.5342264074512958, 0.6444910253789263, 0.06994207708238394, 0.07031762108627508, 0.975284396180421, 0.3330933672678453, 0.6548751599030472, 0.6883607161727554, 0.7481525995594276, 0.8233079505843094, 0.049847514475661533, 0.8175767688800384, 0.9555168998044561, 0.4416155216814475, 0.50827030077151, 0.557718751863934, 0.7306450624288349, 0.591876214888619, 0.7954284725208373, 0.343167011586078, 0.6210778846396752, 0.8656511427700855, 0.4635876284003781, 0.6255982117175033, 0.3193732723533407, 0.8081170724080773, 0.4825077993541566, 0.6165622076141896, 0.6988201996356742, 0.32884601885310216, 0.9856595435792165, 0.696421903772509, 0.4560924063374713, 0.42725963061497163, 0.08383381969744197, 0.2077415257712788, 0.9790522285786848, 0.3927916545740424, 0.7964211617137307, 0.3075272083529113, 0.3463422474072504, 0.5997047680883608, 0.5164073914864976, 0.06373012595452565, 0.2960178111137084, 0.9561072908686538, 0.7280916347362891, 0.1671149041779517, 0.2732765085086133, 0.31600261191243156, 0.2966794663415275, 0.5199778483367261, 0.3623305768543106, 0.24217830399383525, 0.7462374755075427, 0.4982668907967608, 0.8346458157020699, 0.3864047676767218, 0.1270173881341331, 0.7034121639286368, 0.885136466210106, 0.8417622079200704, 0.15486663713295507, 0.14461832446857006, 0.5094576245545838, 0.11995196764307592, 0.29433884619236994, 0.8415013480481901, 0.3692771973516845, 0.8541732962999645, 0.3532017345023631, 0.5407707061962475, 0.6383370849251492, 0.02555813087953048, 0.7693113559707646, 0.3191635911279431, 0.43022885862712534, 0.8982564918447705, 0.8512805777664756, 0.08803118087190352, 0.4191114125657772, 0.3450519951230082, 0.28201614684640014, 0.41285817804034947, 0.7970885259952701, 0.5918617417405887, 0.2890328549989893, 0.3635644756011644, 0.40664218841848826, 0.3256368789826021, 0.7974745880305864, 0.0886946495262358, 0.15338256108858994, 0.9160296375772432, 0.5909810968778575, 0.29854324511402025, 0.5834281366539464, 0.41672990389505027, 0.3019358773596531, 0.2288957744870067, 0.3909701016850263, 0.417599222241712, 0.7562145024717724, 0.2483826991232367, 0.10500247040896708, 0.9136412860767081, 0.6183241460826087, 0.21845035736708104, 0.21981495026107936, 0.18144914169396992, 0.690784061384462, 0.5056455819573025, 0.13164786521769467, 0.7180547992252966, 0.7867435495116287, 0.7712918790368031, 0.9538994830466437, 0.08108274264945914, 0.0971672636759488, 0.8337034014571255, 0.5154526253923705, 0.1327703943955495, 0.25343993184153224, 0.39283872248756535, 0.021054028664334225, 0.7437682962142692, 0.4529511057281349, 0.9167396897965363, 0.1692315090326026, 0.9656698196394212, 0.7191171113028992, 0.8432320186297602, 0.4619749773461368, 0.17394519190771104, 0.5383815285762906, 0.8791815251391734, 0.30133463677363564, 0.435366070937406, 0.6950066911262015, 0.5831072839415583, 0.5812052542119974}
  2. Element(cookiesSelected, Length[cookiesSelected]) → currentCookieIndex
  3. Zip(3 < animateControl < maxAnimate ∧ Defined[IndexOf[A, currentCookieIngredientsIndex]], A, {1, 2, 3, 4, 5, 6}) → highlightLabel
  4. Take(allRandomSeeds, maxRandIndex - numRandoms + 1, maxRandIndex) → currentRandomSeeds
  5. If(countQuestion ≤ 1, 7, 2 + floor((currentRandomSeeds(2) * 12))) → numCookies
  6. Take(Element[possibleOrders, orderIndex], 1, numCookies) → cookieIndex
  7. Zip(Element[cookieImages, A], A, cookieIndex) → chosenCookieImages
  8. PixelsToPoint(Corner[1], Corner[3], Corner[5], (800 - 16, 500 - 16 - 36 - 16)) → bagBottomRight
  9. PixelsToPoint(Corner[1], Corner[3], Corner[5], (435, 500 - 16 - 36 - 16)) → BagBottomLeft
  10. Translate(listFirstCookieLocations, Vector[CookieStart, CookieStart + (0, (imgSize * 2) + (imgSpace * 2))]) → listSecondCookieLocations
  11. Join({listFirstCookieLocations, listSecondCookieLocations}) → listCookieLocations
  12. Zip(Translate[A, Vector[B]], A, chosenCookieImages, Vector[B], Zip[Vector[ImageStart, K], K, listCookieLocations]) → TranslatedCookieImages
  13. Element(TranslatedCookieImages, 13) → cookieImg13
  14. Element(TranslatedCookieImages, 12) → cookieImg12
  15. Element(TranslatedCookieImages, 11) → cookieImg11
  16. Element(TranslatedCookieImages, 10) → cookieImg10
  17. Element(TranslatedCookieImages, 9) → cookieImg9
  18. Element(TranslatedCookieImages, 8) → cookieImg8
  19. Element(TranslatedCookieImages, 7) → cookieImg7
  20. Element(TranslatedCookieImages, 6) → cookieImg6
  21. Element(TranslatedCookieImages, 5) → cookieImg5
  22. Element(TranslatedCookieImages, 4) → cookieImg4
  23. Element(TranslatedCookieImages, 3) → cookieImg3
  24. Element(TranslatedCookieImages, 2) → cookieImg2
  25. Element(TranslatedCookieImages, 1) → cookieImg1
  26. Zip(axisOrigin + (0.5 + A, If[B, 0.45, 0.2]), A, {0, 1, 2, 3, 4, 5}, B, highlightLabel) → horizontalLabelLoc
  27. Zip(horizontalLabelLoc(A), A, currentCookieIngredientsIndex) → currentCookieIngredientsLocFinal
  28. Textfield(input1) → InputBox1
  29. Corner(5) → layoutAppSize
  30. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  31. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  32. Zip(Element[cookieNames, A], A, cookieIndex) → chosenCookieNames
  33. Element(cookieNames, chosenCookieIndex) → chosenCookies
  34. Flatten(Zip[Element[cookieIngredients, K], K, Take[cookiesSelected, 1, If[animateControl ≟ maxAnimate, Length[cookiesSelected], Length[cookiesSelected] - 1]]]) → ingredientFrequencyList
  35. Element(listCookieLocations, IndexOf[currentCookieIndex, cookieIndex]) → currentCookieLocationBag
  36. Segment(axisOrigin, (Length[possibleIngredients], 0) + axisOrigin) → horizontalAxis
  37. Sequence(Segment[axisOrigin + (0, ((0.1 * k) * axisHeight)), axisOrigin + (Length[possibleIngredients], ((0.1 * k) * axisHeight))], k, 1, 10) → horizontalLines
  38. Segment(axisOrigin, (x(axisOrigin), axisHeight + 0.25)) → verticalAxis
  39. Zip(Text[A, B + (-0.05, 0.05), true, true, -1, 0], A, Sequence[(k * 0.2), k, 1, 5], B, Sequence[axisOrigin + (k * (0, (0.2 * axisHeight))), k, 1, 5]) → verticalLabelsPercent
  40. Sequence(Segment[axisOrigin + (-0.1, ((0.2 * k) * axisHeight)), axisOrigin + (0.1, ((0.2 * k) * axisHeight))], k, 1, 5) → horizontalTicks
  41. Min(1, animateControl) → animateCookie
  42. Min(Max[0, animateControl - 2], 1) → animateIngredientsA
  43. Vector(currentCookieLocationBag, currentCookieLocation) → cookieVector
  44. Translate(Element[cookieImages, currentCookieIndex], Vector[ImageStart, currentCookieLocationBag + (animateCookie * cookieVector)]) → chosenCookieImage
  45. Zip(possibleIngredients(A), A, currentCookieIngredientsIndex) → currentCookieIngredients
  46. Zip(Vector[middleCookieLocation, A], A, currentCookieIngredientsLocFinal) → currentCookieIngredientsVec
  47. Sequence(Length[KeepIf[x ≟ A, ingredientFrequencyList]], A, 1, 6) → ingredientObservations
  48. If(animateControl ≟ maxAnimate, numTrials, numTrials - 1) → numTrialsFinal
  49. Zip((A / numTrialsFinal * axisHeight), A, ingredientObservations) → ingredientProbability
  50. BarChart({1, 2, 3, 4, 5, 6}, ingredientProbability, 0.5) → barChartPercents
  51. If(Max[ingredientObservations] ≤ 5, 5, (ceil(Max[ingredientObservations] / 10) * 10)) → frequencyHeight
  52. BarChart(ingredientFrequencyList, 0.5, axisHeight / frequencyHeight) → barChartFrequency
  53. Zip(Text[A, B + (-0.05, 0.05), true, true, -1, 0], A, Sequence[(k * frequencyHeight / 5), k, 1, 5], B, Sequence[axisOrigin + (k * (0, (0.2 * axisHeight))), k, 1, 5]) → verticalLabelsFrequency
  54. PixelsToPoint(Corner[1], Corner[3], Corner[5], (435, 60)) → BagTopLeft
  55. expandCircle(listCookieLocations(numCookies) + (imgSize / 2, imgSize / 2), 26 + (8 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingCircle
  56. Zip((("SetFixed(cookieImg" * A) * ",true,true)"), A, Sequence[13]) → cmdUnfixCookieImgs
  57. Zip((("SetFixed(cookieImg" * A) * ",true,false)"), A, Sequence[13]) → cmdFixCookieImgs
  58. Min(Max[0, animateControl - 1], 1) → animateIngredientsB
  59. Zip(middleCookieLocation + (A, -0.5), A, cookieStartOffsets) → ingredientStartPositions
  60. Zip(Text[RotateText[A, pi / 2], B + (animateIngredientsA * (C - B)), true, true, 0, -1], A, currentCookieIngredients, B, ingredientStartPositions, C, currentCookieIngredientsLocFinal) → currentCookieIngredientsText
  61. Zip(Text[((If[C, "\textbf{", ""] * RotateText[A, pi / 2]) * If[C, "}", ""]), B, true, true, 0, -1], A, possibleIngredients, B, horizontalLabelLoc, C, highlightLabel) → horizonalLabels

AI 绘图提示语参考

绘制一个包含多个巧克力饼干的袋子，每个饼干上都有不同的配料，如巧克力碎片、坚果和糖粒。在袋子下方，绘制一个条形图，展示每种配料的频率。条形图的底部是配料名称，顶部是相应的频率高度。动画控制饼干从袋子中随机取出，并在条形图中更新配料的频率。
以上提示语为根据原始绘图命令整理而来，仅供参考。