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Envelope Matching Probability Simulation

Envelope Matching Probability Simulation
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2016-06-09 01:16
SequenceLimitProbability & StatisticsGraphing
In collections Statistics Simulations Statistics Simulations
This example demonstrates the classic Envelope Matching Problem (Derangements), simulating the probability of matching letters to envelopes through random assignment. Core concepts include probability statistics, permutations, and derangement formulas. Construction utilizes Sequence to generate letter lists, Shuffle for randomization, If for matching logic, Sum to count matches, and DotPlot for distribution visualization. Suitable for high school mathematics classrooms or self-study in probability, offering an intuitive understanding of random events and limiting probabilities.

GeoGebra Commands & Parameters

  1. Sequence(n, n, 1, 25) → letter
  2. Shuffle(letter) → list1
  3. If(A2 ≟ B2, 1, 0) → C2
  4. If(A3 ≟ B3, 1, 0) → C3
  5. If(A4 ≟ B4, 1, 0) → C4
  6. If(A5 ≟ B5, 1, 0) → C5
  7. If(A6 ≟ B6, 1, 0) → C6
  8. If(A7 ≟ B7, 1, 0) → C7
  9. If(A8 ≟ B8, 1, 0) → C8
  10. If(A9 ≟ B9, 1, 0) → C9
  11. If(A10 ≟ B10, 1, 0) → C10
  12. If(A11 ≟ B11, 1, 0) → C11
  13. If(A12 ≟ B12, 1, 0) → C12
  14. If(A13 ≟ B13, 1, 0) → C13
  15. If(A14 ≟ B14, 1, 0) → C14
  16. If(A15 ≟ B15, 1, 0) → C15
  17. If(A16 ≟ B16, 1, 0) → C16
  18. If(A17 ≟ B17, 1, 0) → C17
  19. If(A18 ≟ B18, 1, 0) → C18
  20. If(A19 ≟ B19, 1, 0) → C19
  21. If(A20 ≟ B20, 1, 0) → C20
  22. If(A21 ≟ B21, 1, 0) → C21
  23. If(A22 ≟ B22, 1, 0) → C22
  24. If(A23 ≟ B23, 1, 0) → C23
  25. If(A24 ≟ B24, 1, 0) → C24
  26. If(A25 ≟ B25, 1, 0) → C25
  27. If(A26 ≟ B26, 1, 0) → C26
  28. Sum(C2:C26) → D2
  29. DotPlot(data, false, 0.2) → list2

AI Drawing Prompt Reference

Create a dot plot simulating the envelope matching problem. Generate a sequence of numbers from 1 to 25 representing letters, then randomly shuffle them to represent envelopes. For each position, compare the letter number with the envelope number; if they match, record 1, otherwise 0. Sum all matches to get the total number of correct matches for one trial. Repeat this process many times, and plot the distribution of match counts as dots on a graph, with the x-axis showing the number of matches (0 to 25) and the y-axis showing frequency or density, revealing the probability distribution of matching counts.
The prompt above was compiled from the original drawing commands and is for reference only.