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Laplace Probability and Random Number Generator

Laplace Probability and Random Number Generator
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2025-05-14 19:36
In collections Laplace-Wahrscheinlichkeit
This example demonstrates the calculation of Laplace probabilities using a random number generator. The core math concepts involve probability & statistics, specifically Laplace probabilities and their application in single-stage random experiments. Key GeoGebra commands and objects used in the construction include Shuffle, If, Element, Random, Textfield, Join, Sequence, and Text to generate rando

GeoGebra Commands & Parameters

  1. Shuffle(1…numberOfQuestions) → Reihenfolge1, {10, 4, 1, 9, 2, 5, 8, 3, 6, 12, 11, 7}
  2. If(abs(IndexOf[1, Reihenfolge1] - IndexOf[5, Reihenfolge1]) ≠ 1, Reihenfolge1, If[¬(12 ∈ {IndexOf[1, Reihenfolge1], IndexOf[5, Reihenfolge1]}), Join[{Take[Reihenfolge1, 1, Min[IndexOf[1, Reihenfolge1], IndexOf[5, Reihenfolge1]]], {Reihenfolge1(12)}, Take[Reihenfolge1, Min[IndexOf[1, Reihenfolge1], IndexOf[5, Reihenfolge1]] + 1, 11]}], Join[{Take[Reihenfolge1, 2, Min[IndexOf[1, Reihenfolge1], IndexOf[5, Reihenfolge1]]], {Reihenfolge1(1)}, Take[Reihenfolge1, Min[IndexOf[1, Reihenfolge1], IndexOf[5, Reihenfolge1]] + 1, 12]}]]) → randomQuestions
  3. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  4. Random(16, 16, 12) → SolutionList2, {16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16}
  5. If(questionCount < 3, input1 ≟ SolutionList1(randomQuestion), input1 ≟ SolutionList1(randomQuestion) ∧ input2 ≟ SolutionList2(randomQuestion) ∨ input1 / input2 ≟ SolutionList1(randomQuestion) / SolutionList2(randomQuestion)) → correct2
  6. If(step ≟ 1, correct1, step ≟ 2, correct2, false) → correct
  7. Textfield(input) → inputBox
  8. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  9. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  10. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-14.020000000000017, 8.279999999999994), (-13.01764150943398, 8.279999999999994), (-12.015283018867944, 8.279999999999994), (-11.012924528301905, 8.279999999999994), (-10.010566037735869, 8.279999999999994), (-9.008207547169832, 8.279999999999994), (-8.005849056603793, 8.279999999999994), (-7.003490566037757, 8.279999999999994), (-6.00113207547172, 8.279999999999994), (-4.998773584905683, 8.279999999999994), (-3.996415094339646, 8.279999999999994), (-2.9940566037736094, 8.279999999999994), (-1.9916981132075708, 8.279999999999994), (-0.9893396226415341, 8.279999999999994), (0.013018867924502686, 8.279999999999994), (1.0153773584905395, 8.279999999999994), (2.017735849056578, 8.279999999999994), (3.020094339622613, 8.279999999999994)}, {(-14.020000000000017, 7.276913580246909), (-13.01764150943398, 7.276913580246909), (-12.015283018867944, 7.276913580246909), (-11.012924528301905, 7.276913580246909), (-10.010566037735869, 7.276913580246909), (-9.008207547169832, 7.276913580246909), (-8.005849056603793, 7.276913580246909), (-7.003490566037757, 7.276913580246909), (-6.00113207547172, 7.276913580246909), (-4.998773584905683, 7.276913580246909), (-3.996415094339646, 7.276913580246909), (-2.9940566037736094, 7.276913580246909), (-1.9916981132075708, 7.276913580246909), (-0.9893396226415341, 7.276913580246909), (0.013018867924502686, 7.276913580246909), (1.0153773584905395, 7.276913580246909), (2.017735849056578, 7.276913580246909), (3.020094339622613, 7.276913580246909)}, {(-14.020000000000017, 6.2738271604938225), (-13.01764150943398, 6.2738271604938225), (-12.015283018867944, 6.2738271604938225), (-11.012924528301905, 6.2738271604938225), (-10.010566037735869, 6.2738271604938225), (-9.008207547169832, 6.2738271604938225), (-8.005849056603793, 6.2738271604938225), (-7.003490566037757, 6.2738271604938225), (-6.00113207547172, 6.2738271604938225), (-4.998773584905683, 6.2738271604938225), (-3.996415094339646, 6.2738271604938225), (-2.9940566037736094, 6.2738271604938225), (-1.9916981132075708, 6.2738271604938225), (-0.9893396226415341, 6.2738271604938225), (0.013018867924502686, 6.2738271604938225), (1.0153773584905395, 6.2738271604938225), (2.017735849056578, 6.2738271604938225), (3.020094339622613, 6.2738271604938225)}, {(-14.020000000000017, 5.270740740740737), (-13.01764150943398, 5.270740740740737), (-12.015283018867944, 5.270740740740737), (-11.012924528301905, 5.270740740740737), (-10.010566037735869, 5.270740740740737), (-9.008207547169832, 5.270740740740737), (-8.005849056603793, 5.270740740740737), (-7.003490566037757, 5.270740740740737), (-6.00113207547172, 5.270740740740737), (-4.998773584905683, 5.270740740740737), (-3.996415094339646, 5.270740740740737), (-2.9940566037736094, 5.270740740740737), (-1.9916981132075708, 5.270740740740737), (-0.9893396226415341, 5.270740740740737), (0.013018867924502686, 5.270740740740737), (1.0153773584905395, 5.270740740740737), (2.017735849056578, 5.270740740740737), (3.020094339622613, 5.270740740740737)}, {(-14.020000000000017, 4.267654320987651), (-13.01764150943398, 4.267654320987651), (-12.015283018867944, 4.267654320987651), (-11.012924528301905, 4.267654320987651), (-10.010566037735869, 4.267654320987651), (-9.008207547169832, 4.267654320987651), (-8.005849056603793, 4.267654320987651), (-7.003490566037757, 4.267654320987651), (-6.00113207547172, 4.267654320987651), (-4.998773584905683, 4.267654320987651), (-3.996415094339646, 4.267654320987651), (-2.9940566037736094, 4.267654320987651), (-1.9916981132075708, 4.267654320987651), (-0.9893396226415341, 4.267654320987651), (0.013018867924502686, 4.267654320987651), (1.0153773584905395, 4.267654320987651), (2.017735849056578, 4.267654320987651), (3.020094339622613, 4.267654320987651)}, {(-14.020000000000017, 3.2645679012345656), (-13.01764150943398, 3.2645679012345656), (-12.015283018867944, 3.2645679012345656), (-11.012924528301905, 3.2645679012345656), (-10.010566037735869, 3.2645679012345656), (-9.008207547169832, 3.2645679012345656), (-8.005849056603793, 3.2645679012345656), (-7.003490566037757, 3.2645679012345656), (-6.00113207547172, 3.2645679012345656), (-4.998773584905683, 3.2645679012345656), (-3.996415094339646, 3.2645679012345656), (-2.9940566037736094, 3.2645679012345656), (-1.9916981132075708, 3.2645679012345656), (-0.9893396226415341, 3.2645679012345656), (0.013018867924502686, 3.2645679012345656), (1.0153773584905395, 3.2645679012345656), (2.017735849056578, 3.2645679012345656), (3.020094339622613, 3.2645679012345656)}, {(-14.020000000000017, 2.2614814814814803), (-13.01764150943398, 2.2614814814814803), (-12.015283018867944, 2.2614814814814803), (-11.012924528301905, 2.2614814814814803), (-10.010566037735869, 2.2614814814814803), (-9.008207547169832, 2.2614814814814803), (-8.005849056603793, 2.2614814814814803), (-7.003490566037757, 2.2614814814814803), (-6.00113207547172, 2.2614814814814803), (-4.998773584905683, 2.2614814814814803), (-3.996415094339646, 2.2614814814814803), (-2.9940566037736094, 2.2614814814814803), (-1.9916981132075708, 2.2614814814814803), (-0.9893396226415341, 2.2614814814814803), (0.013018867924502686, 2.2614814814814803), (1.0153773584905395, 2.2614814814814803), (2.017735849056578, 2.2614814814814803), (3.020094339622613, 2.2614814814814803)}, {(-14.020000000000017, 1.258395061728394), (-13.01764150943398, 1.258395061728394), (-12.015283018867944, 1.258395061728394), (-11.012924528301905, 1.258395061728394), (-10.010566037735869, 1.258395061728394), (-9.008207547169832, 1.258395061728394), (-8.005849056603793, 1.258395061728394), (-7.003490566037757, 1.258395061728394), (-6.00113207547172, 1.258395061728394), (-4.998773584905683, 1.258395061728394), (-3.996415094339646, 1.258395061728394), (-2.9940566037736094, 1.258395061728394), (-1.9916981132075708, 1.258395061728394), (-0.9893396226415341, 1.258395061728394), (0.013018867924502686, 1.258395061728394), (1.0153773584905395, 1.258395061728394), (2.017735849056578, 1.258395061728394), (3.020094339622613, 1.258395061728394)}, {(-14.020000000000017, 0.2553086419753079), (-13.01764150943398, 0.2553086419753079), (-12.015283018867944, 0.2553086419753079), (-11.012924528301905, 0.2553086419753079), (-10.010566037735869, 0.2553086419753079), (-9.008207547169832, 0.2553086419753079), (-8.005849056603793, 0.2553086419753079), (-7.003490566037757, 0.2553086419753079), (-6.00113207547172, 0.2553086419753079), (-4.998773584905683, 0.2553086419753079), (-3.996415094339646, 0.2553086419753079), (-2.9940566037736094, 0.2553086419753079), (-1.9916981132075708, 0.2553086419753079), (-0.9893396226415341, 0.2553086419753079), (0.013018867924502686, 0.2553086419753079), (1.0153773584905395, 0.2553086419753079), (2.017735849056578, 0.2553086419753079), (3.020094339622613, 0.2553086419753079)}, {(-14.020000000000017, -0.7477777777777774), (-13.01764150943398, -0.7477777777777774), (-12.015283018867944, -0.7477777777777774), (-11.012924528301905, -0.7477777777777774), (-10.010566037735869, -0.7477777777777774), (-9.008207547169832, -0.7477777777777774), (-8.005849056603793, -0.7477777777777774), (-7.003490566037757, -0.7477777777777774), (-6.00113207547172, -0.7477777777777774), (-4.998773584905683, -0.7477777777777774), (-3.996415094339646, -0.7477777777777774), (-2.9940566037736094, -0.7477777777777774), (-1.9916981132075708, -0.7477777777777774), (-0.9893396226415341, -0.7477777777777774), (0.013018867924502686, -0.7477777777777774), (1.0153773584905395, -0.7477777777777774), (2.017735849056578, -0.7477777777777774), (3.020094339622613, -0.7477777777777774)}, {(-14.020000000000017, -1.7508641975308628), (-13.01764150943398, -1.7508641975308628), (-12.015283018867944, -1.7508641975308628), (-11.012924528301905, -1.7508641975308628), (-10.010566037735869, -1.7508641975308628), (-9.008207547169832, -1.7508641975308628), (-8.005849056603793, -1.7508641975308628), (-7.003490566037757, -1.7508641975308628), (-6.00113207547172, -1.7508641975308628), (-4.998773584905683, -1.7508641975308628), (-3.996415094339646, -1.7508641975308628), (-2.9940566037736094, -1.7508641975308628), (-1.9916981132075708, -1.7508641975308628), (-0.9893396226415341, -1.7508641975308628), (0.013018867924502686, -1.7508641975308628), (1.0153773584905395, -1.7508641975308628), (2.017735849056578, -1.7508641975308628), (3.020094339622613, -1.7508641975308628)}, {(-14.020000000000017, -2.753950617283948), (-13.01764150943398, -2.753950617283948), (-12.015283018867944, -2.753950617283948), (-11.012924528301905, -2.753950617283948), (-10.010566037735869, -2.753950617283948), (-9.008207547169832, -2.753950617283948), (-8.005849056603793, -2.753950617283948), (-7.003490566037757, -2.753950617283948), (-6.00113207547172, -2.753950617283948), (-4.998773584905683, -2.753950617283948), (-3.996415094339646, -2.753950617283948), (-2.9940566037736094, -2.753950617283948), (-1.9916981132075708, -2.753950617283948), (-0.9893396226415341, -2.753950617283948), (0.013018867924502686, -2.753950617283948), (1.0153773584905395, -2.753950617283948), (2.017735849056578, -2.753950617283948), (3.020094339622613, -2.753950617283948)}, {(-14.020000000000017, -3.7570370370370334), (-13.01764150943398, -3.7570370370370334), (-12.015283018867944, -3.7570370370370334), (-11.012924528301905, -3.7570370370370334), (-10.010566037735869, -3.7570370370370334), (-9.008207547169832, -3.7570370370370334), (-8.005849056603793, -3.7570370370370334), (-7.003490566037757, -3.7570370370370334), (-6.00113207547172, -3.7570370370370334), (-4.998773584905683, -3.7570370370370334), (-3.996415094339646, -3.7570370370370334), (-2.9940566037736094, -3.7570370370370334), (-1.9916981132075708, -3.7570370370370334), (-0.9893396226415341, -3.7570370370370334), (0.013018867924502686, -3.7570370370370334), (1.0153773584905395, -3.7570370370370334), (2.017735849056578, -3.7570370370370334), (3.020094339622613, -3.7570370370370334)}, {(-14.020000000000017, -4.7601234567901205), (-13.01764150943398, -4.7601234567901205), (-12.015283018867944, -4.7601234567901205), (-11.012924528301905, -4.7601234567901205), (-10.010566037735869, -4.7601234567901205), (-9.008207547169832, -4.7601234567901205), (-8.005849056603793, -4.7601234567901205), (-7.003490566037757, -4.7601234567901205), (-6.00113207547172, -4.7601234567901205), (-4.998773584905683, -4.7601234567901205), (-3.996415094339646, -4.7601234567901205), (-2.9940566037736094, -4.7601234567901205), (-1.9916981132075708, -4.7601234567901205), (-0.9893396226415341, -4.7601234567901205), (0.013018867924502686, -4.7601234567901205), (1.0153773584905395, -4.7601234567901205), (2.017735849056578, -4.7601234567901205), (3.020094339622613, -4.7601234567901205)}}
  11. Textfield(input1) → InputBox1
  12. Textfield(input2) → InputBox2
  13. If(step ≟ 1, Defined[input], step ≟ 2 ∧ questionCount < 3, Defined[input1], Defined[input1] ∧ Defined[input2]) → clickableBtnValidate
  14. Text(txtCounter, Midpoint[Corner[imgRandom, 1], Corner[imgRandom, 3]] + (0, 0.05), false, true, 0, 0) → txtCounter1