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Dice Roll Probability Distribution Simulation

Dice Roll Probability Distribution Simulation
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2020-10-15 16:55
SequenceProbability & StatisticsSlider Animation
This GeoGebra example demonstrates the probability distribution simulation of rolling two dice and summing the results. Core mathematical concepts include: random variable probability distribution, frequency statistics, and the law of large numbers. Construction details: ①Use the Random command to generate random numbers simulating dice rolls; ②Use the Sequence command to generate multiple experiment sequences; ③Use CountIf to count frequencies of sums (2-12); ④Use Polygon to draw frequency distribution or data lists for results; ⑤Set up interactive buttons (button1, button2) to control simulation. Suitable for middle and high school mathematics probability and statistics teaching, demonstrating discrete random variable distributions and the relationship between frequency and probability.

GeoGebra Commands & Parameters

  1. CountIf(x ≟ 2, data) → two
  2. CountIf(x ≟ 3, data) → three
  3. CountIf(x ≟ 6, data) → six
  4. CountIf(x ≟ 5, data) → five
  5. CountIf(x ≟ 4, data) → four
  6. CountIf(x ≟ 7, data) → seven
  7. CountIf(x ≟ 8, data) → eight
  8. CountIf(x ≟ 9, data) → nine
  9. CountIf(x ≟ 10, data) → ten
  10. CountIf(x ≟ 11, data) → eleven
  11. CountIf(x ≟ 12, data) → twelve
  12. Sequence((7, i), i, 1, seven) → list7
  13. Sequence((12, i), i, 1, twelve) → list12
  14. Sequence((11, i), i, 1, eleven) → list11
  15. Sequence((10, i), i, 1, ten) → list10
  16. Sequence((9, i), i, 1, nine) → list9
  17. Sequence((8, i), i, 1, eight) → list8
  18. Sequence((6, i), i, 1, six) → list6
  19. Sequence((5, i), i, 1, five) → list5
  20. Sequence((4, i), i, 1, four) → list4
  21. Sequence((3, i), i, 1, three) → list3
  22. Sequence((2, i), i, 1, two) → list2
  23. Random(1, 6) → b
  24. Random(1, 6) → a
  25. Point(xAxis) → C
  26. Polygon(A, B, C) → t1, c, a_1, b_1

AI Drawing Prompt Reference

Draw a probability distribution chart for the sum of two dice rolls. The horizontal axis shows possible sums from 2 to 12, and the vertical axis shows frequency counts. Represent each sum's frequency with vertical stacks of dots or short lines, forming a bar-like distribution. Include a slider to control the number of trials and two buttons to reroll or reset the statistics. Frequencies accumulate over many random trials, illustrating how empirical frequencies approach theoretical probabilities as trials increase.
The prompt above was compiled from the original drawing commands and is for reference only.