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Head or Tail? Simulating Relative Frequency of Coin Tosses

Head or Tail? Simulating Relative Frequency of Coin Tosses
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2014-02-14 07:26
FunctionSequenceProbability & StatisticsSlider AnimationGraphing
This GeoGebra example dynamically simulates a coin-tossing experiment, demonstrating how the relative frequency of heads converges toward the theoretical probability of 0.5 as the number of trials increases. The core mathematical concept is the Law of Large Numbers and the stability of relative frequency in probability theory, linking random experiments to empirical probability. Construction details: the Random command generates random values (0 or 1 representing tails or heads), Sequence builds a series of trials, and Element extracts each outcome. Multiple objects (A1 through A39) track cumulative head counts, enabling real-time calculation and visualization of relative frequency. Suitable for high school or introductory college probability and statistics courses, this interactive tool helps students grasp the statistical meaning of frequency-based probability estimation and explore the behavior of random phenomena.

GeoGebra Commands & Parameters

  1. Random(0, 1) → d
  2. Random(0, 1) → A1
  3. Random(0, 1) → A2
  4. Random(0, 1) → A3
  5. Random(0, 1) → A4
  6. Random(0, 1) → A5
  7. Random(0, 1) → A6
  8. Random(0, 1) → A7
  9. Random(0, 1) → A8
  10. Random(0, 1) → A9
  11. Random(0, 1) → A10
  12. Random(0, 1) → A11
  13. Random(0, 1) → A12
  14. Random(0, 1) → A13
  15. Random(0, 1) → A14
  16. Random(0, 1) → A15
  17. Random(0, 1) → A16
  18. Random(0, 1) → A17
  19. Random(0, 1) → A18
  20. Random(0, 1) → A19
  21. Random(0, 1) → A20
  22. Random(0, 1) → A21
  23. Random(0, 1) → A22
  24. Random(0, 1) → A23
  25. Random(0, 1) → A24
  26. Random(0, 1) → A25
  27. Random(0, 1) → A26
  28. Random(0, 1) → A27
  29. Random(0, 1) → A28
  30. Random(0, 1) → A29
  31. Random(0, 1) → A30
  32. Random(0, 1) → A31
  33. Random(0, 1) → A32
  34. Random(0, 1) → A33
  35. Random(0, 1) → A34
  36. Random(0, 1) → A35
  37. Random(0, 1) → A36
  38. Random(0, 1) → A37
  39. Random(0, 1) → A38
  40. Random(0, 1) → A39
  41. Random(0, 1) → A40
  42. Random(0, 1) → A41
  43. Random(0, 1) → A42
  44. Random(0, 1) → A43
  45. Random(0, 1) → A44
  46. Random(0, 1) → A45
  47. Random(0, 1) → A46
  48. Random(0, 1) → A47
  49. Random(0, 1) → A48
  50. Random(0, 1) → A49
  51. Random(0, 1) → A50
  52. Random(0, 1) → A51
  53. Random(0, 1) → A52
  54. Random(0, 1) → A53
  55. Random(0, 1) → A54
  56. Random(0, 1) → A55
  57. Random(0, 1) → A56
  58. Random(0, 1) → A57
  59. Random(0, 1) → A58
  60. Random(0, 1) → A59
  61. Random(0, 1) → A60
  62. Random(0, 1) → A61
  63. Random(0, 1) → A62
  64. Random(0, 1) → A63
  65. Random(0, 1) → A64
  66. Random(0, 1) → A65
  67. Random(0, 1) → A66
  68. Random(0, 1) → A67
  69. Random(0, 1) → A68
  70. Random(0, 1) → A69
  71. Random(0, 1) → A70
  72. Random(0, 1) → A71
  73. Random(0, 1) → A72
  74. Random(0, 1) → A73
  75. Random(0, 1) → A74
  76. Random(0, 1) → A75
  77. Random(0, 1) → A76
  78. Random(0, 1) → A77
  79. Random(0, 1) → A78
  80. Random(0, 1) → A79
  81. Random(0, 1) → A80
  82. Random(0, 1) → A81
  83. Random(0, 1) → A82
  84. Random(0, 1) → A83
  85. Random(0, 1) → A84
  86. Random(0, 1) → A85
  87. Random(0, 1) → A86
  88. Random(0, 1) → A87
  89. Random(0, 1) → A88
  90. Random(0, 1) → A89
  91. Random(0, 1) → A90
  92. Random(0, 1) → A91
  93. Random(0, 1) → A92
  94. Random(0, 1) → A93
  95. Random(0, 1) → A94
  96. Random(0, 1) → A95
  97. Random(0, 1) → A96
  98. Random(0, 1) → A97
  99. Random(0, 1) → A98
  100. Random(0, 1) → A99
  101. Random(0, 1) → A100
  102. Random(0, 1) → A101
  103. Random(0, 1) → A102
  104. Random(0, 1) → A103
  105. Random(0, 1) → A104
  106. Random(0, 1) → A105
  107. Random(0, 1) → A106
  108. Random(0, 1) → A107
  109. Random(0, 1) → A108
  110. Random(0, 1) → A109
  111. Random(0, 1) → A110
  112. Random(0, 1) → A111
  113. Random(0, 1) → A112
  114. Random(0, 1) → A113
  115. Random(0, 1) → A114
  116. Random(0, 1) → A115
  117. Random(0, 1) → A116
  118. Random(0, 1) → A117
  119. Random(0, 1) → A118
  120. Random(0, 1) → A119
  121. Random(0, 1) → A120
  122. Random(0, 1) → A121
  123. Random(0, 1) → A122
  124. Random(0, 1) → A123
  125. Random(0, 1) → A124
  126. Random(0, 1) → A125
  127. Random(0, 1) → A126
  128. Random(0, 1) → A127
  129. Random(0, 1) → A128
  130. Random(0, 1) → A129
  131. Random(0, 1) → A130
  132. Random(0, 1) → A131
  133. Random(0, 1) → A132
  134. Random(0, 1) → A133
  135. Random(0, 1) → A134
  136. Random(0, 1) → A135
  137. Random(0, 1) → A136
  138. Random(0, 1) → A137
  139. Random(0, 1) → A138
  140. Random(0, 1) → A139
  141. Random(0, 1) → A140
  142. Random(0, 1) → A141
  143. Random(0, 1) → A142
  144. Random(0, 1) → A143
  145. Random(0, 1) → A144
  146. Random(0, 1) → A145
  147. Random(0, 1) → A146
  148. Random(0, 1) → A147
  149. Random(0, 1) → A148
  150. Random(0, 1) → A149
  151. Random(0, 1) → A150
  152. Random(0, 1) → A151
  153. Random(0, 1) → A152
  154. Random(0, 1) → A153
  155. Random(0, 1) → A154
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  157. Random(0, 1) → A156
  158. Random(0, 1) → A157
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  162. Random(0, 1) → A161
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  164. Random(0, 1) → A163
  165. Random(0, 1) → A164
  166. Random(0, 1) → A165
  167. Random(0, 1) → A166
  168. Random(0, 1) → A167
  169. Random(0, 1) → A168
  170. Random(0, 1) → A169
  171. Random(0, 1) → A170
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  173. Random(0, 1) → A172
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  175. Random(0, 1) → A174
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  177. Random(0, 1) → A176
  178. Random(0, 1) → A177
  179. Random(0, 1) → A178
  180. Random(0, 1) → A179
  181. Random(0, 1) → A180
  182. Random(0, 1) → A181
  183. Random(0, 1) → A182
  184. Random(0, 1) → A183
  185. Random(0, 1) → A184
  186. Random(0, 1) → A185
  187. Random(0, 1) → A186
  188. Random(0, 1) → A187
  189. Random(0, 1) → A188
  190. Random(0, 1) → A189
  191. Random(0, 1) → A190
  192. Random(0, 1) → A191
  193. Random(0, 1) → A192
  194. Random(0, 1) → A193
  195. Random(0, 1) → A194
  196. Random(0, 1) → A195
  197. Random(0, 1) → A196
  198. Random(0, 1) → A197
  199. Random(0, 1) → A198
  200. Random(0, 1) → A199
  201. Random(0, 1) → A200
  202. Random(0, 1) → A201
  203. Random(0, 1) → A202
  204. Random(0, 1) → A203
  205. Random(0, 1) → A204
  206. Random(0, 1) → A205
  207. Random(0, 1) → A206
  208. Random(0, 1) → A207
  209. Random(0, 1) → A208
  210. Random(0, 1) → A209
  211. Random(0, 1) → A210
  212. Random(0, 1) → A211
  213. Random(0, 1) → A212
  214. Random(0, 1) → A213
  215. Random(0, 1) → A214
  216. Random(0, 1) → A215
  217. Random(0, 1) → A216
  218. Random(0, 1) → A217
  219. Random(0, 1) → A218
  220. Random(0, 1) → A219
  221. Random(0, 1) → A220
  222. Random(0, 1) → A221
  223. Random(0, 1) → A222
  224. Random(0, 1) → A223
  225. Random(0, 1) → A224
  226. Random(0, 1) → A225
  227. Random(0, 1) → A226
  228. Random(0, 1) → A227
  229. Random(0, 1) → A228
  230. Random(0, 1) → A229
  231. Random(0, 1) → A230
  232. Random(0, 1) → A231
  233. Random(0, 1) → A232
  234. Random(0, 1) → A233
  235. Random(0, 1) → A234
  236. Random(0, 1) → A235
  237. Random(0, 1) → A236
  238. Random(0, 1) → A237
  239. Random(0, 1) → A238
  240. Random(0, 1) → A239
  241. Random(0, 1) → A240
  242. Random(0, 1) → A241
  243. Random(0, 1) → A242
  244. Random(0, 1) → A243
  245. Random(0, 1) → A244
  246. Random(0, 1) → A245
  247. Random(0, 1) → A246
  248. Random(0, 1) → A247
  249. Random(0, 1) → A248
  250. Random(0, 1) → A249
  251. Random(0, 1) → A250
  252. Random(0, 1) → A251
  253. Random(0, 1) → A252
  254. Random(0, 1) → A253
  255. Random(0, 1) → A254
  256. Random(0, 1) → A255
  257. Random(0, 1) → A256
  258. Random(0, 1) → A257
  259. Random(0, 1) → A258
  260. Random(0, 1) → A259
  261. Random(0, 1) → A260
  262. Random(0, 1) → A261
  263. Random(0, 1) → A262
  264. Random(0, 1) → A263
  265. Random(0, 1) → A264
  266. Random(0, 1) → A265
  267. Random(0, 1) → A266
  268. Random(0, 1) → A267
  269. Random(0, 1) → A268
  270. Random(0, 1) → A269
  271. Random(0, 1) → A270
  272. Random(0, 1) → A271
  273. Random(0, 1) → A272
  274. Random(0, 1) → A273
  275. Random(0, 1) → A274
  276. Random(0, 1) → A275
  277. Random(0, 1) → A276
  278. Random(0, 1) → A277
  279. Random(0, 1) → A278
  280. Random(0, 1) → A279
  281. Random(0, 1) → A280
  282. Random(0, 1) → A281
  283. Random(0, 1) → A282
  284. Random(0, 1) → A283
  285. Random(0, 1) → A284
  286. Random(0, 1) → A285
  287. Random(0, 1) → A286
  288. Random(0, 1) → A287
  289. Random(0, 1) → A288
  290. Random(0, 1) → A289
  291. Random(0, 1) → A290
  292. Random(0, 1) → A291
  293. Random(0, 1) → A292
  294. Random(0, 1) → A293
  295. Random(0, 1) → A294
  296. Random(0, 1) → A295
  297. Random(0, 1) → A296
  298. Random(0, 1) → A297
  299. Random(0, 1) → A298
  300. Random(0, 1) → A299
  301. Random(0, 1) → A300
  302. Random(0, 1) → A301
  303. Random(0, 1) → A302
  304. Random(0, 1) → A303
  305. Random(0, 1) → A304
  306. Random(0, 1) → A305
  307. Random(0, 1) → A306
  308. Random(0, 1) → A307
  309. Random(0, 1) → A308
  310. Random(0, 1) → A309
  311. Random(0, 1) → A310
  312. Random(0, 1) → A311
  313. Random(0, 1) → A312
  314. Random(0, 1) → A313
  315. Random(0, 1) → A314
  316. Random(0, 1) → A315
  317. Random(0, 1) → A316
  318. Random(0, 1) → A317
  319. Random(0, 1) → A318
  320. Random(0, 1) → A319
  321. Random(0, 1) → A320
  322. Random(0, 1) → A321
  323. Random(0, 1) → A322
  324. Random(0, 1) → A323
  325. Random(0, 1) → A324
  326. Random(0, 1) → A325
  327. Random(0, 1) → A326
  328. Random(0, 1) → A327
  329. Random(0, 1) → A328
  330. Random(0, 1) → A329
  331. Random(0, 1) → A330
  332. Random(0, 1) → A331
  333. Random(0, 1) → A332
  334. Random(0, 1) → A333
  335. Random(0, 1) → A334
  336. Random(0, 1) → A335
  337. Random(0, 1) → A336
  338. Random(0, 1) → A337
  339. Random(0, 1) → A338
  340. Random(0, 1) → A339
  341. Random(0, 1) → A340
  342. Random(0, 1) → A341
  343. Random(0, 1) → A342
  344. Random(0, 1) → A343
  345. Random(0, 1) → A344
  346. Random(0, 1) → A345
  347. Random(0, 1) → A346
  348. Random(0, 1) → A347
  349. Random(0, 1) → A348
  350. Random(0, 1) → A349
  351. Random(0, 1) → A350
  352. Random(0, 1) → A351
  353. Random(0, 1) → A352
  354. Random(0, 1) → A353
  355. Random(0, 1) → A354
  356. Random(0, 1) → A355
  357. Random(0, 1) → A356
  358. Random(0, 1) → A357
  359. Random(0, 1) → A358
  360. Random(0, 1) → A359
  361. Random(0, 1) → A360
  362. Random(0, 1) → A361
  363. Random(0, 1) → A362
  364. Random(0, 1) → A363
  365. Random(0, 1) → A364
  366. Random(0, 1) → A365
  367. Random(0, 1) → A366
  368. Random(0, 1) → A367
  369. Random(0, 1) → A368
  370. Random(0, 1) → A369
  371. Random(0, 1) → A370
  372. Random(0, 1) → A371
  373. Random(0, 1) → A372
  374. Random(0, 1) → A373
  375. Random(0, 1) → A374
  376. Random(0, 1) → A375
  377. Random(0, 1) → A376
  378. Random(0, 1) → A377
  379. Random(0, 1) → A378
  380. Random(0, 1) → A379
  381. Random(0, 1) → A380
  382. Random(0, 1) → A381
  383. Random(0, 1) → A382
  384. Random(0, 1) → A383
  385. Random(0, 1) → A384
  386. Random(0, 1) → A385
  387. Random(0, 1) → A386
  388. Random(0, 1) → A387
  389. Random(0, 1) → A388
  390. Random(0, 1) → A389
  391. Random(0, 1) → A390
  392. Random(0, 1) → A391
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  394. Random(0, 1) → A393
  395. Random(0, 1) → A394
  396. Random(0, 1) → A395
  397. Random(0, 1) → A396
  398. Random(0, 1) → A397
  399. Random(0, 1) → A398
  400. Random(0, 1) → A399
  401. Random(0, 1) → A400
  402. Random(0, 1) → A401
  403. Random(0, 1) → A402
  404. Random(0, 1) → A403
  405. Random(0, 1) → A404
  406. Random(0, 1) → A405
  407. Random(0, 1) → A406
  408. Random(0, 1) → A407
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  410. Random(0, 1) → A409
  411. Random(0, 1) → A410
  412. Random(0, 1) → A411
  413. Random(0, 1) → A412
  414. Random(0, 1) → A413
  415. Random(0, 1) → A414
  416. Random(0, 1) → A415
  417. Random(0, 1) → A416
  418. Random(0, 1) → A417
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  422. Random(0, 1) → A421
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  427. Random(0, 1) → A426
  428. Random(0, 1) → A427
  429. Random(0, 1) → A428
  430. Random(0, 1) → A429
  431. Random(0, 1) → A430
  432. Random(0, 1) → A431
  433. Random(0, 1) → A432
  434. Random(0, 1) → A433
  435. Random(0, 1) → A434
  436. Random(0, 1) → A435
  437. Random(0, 1) → A436
  438. Random(0, 1) → A437
  439. Random(0, 1) → A438
  440. Random(0, 1) → A439
  441. Random(0, 1) → A440
  442. Random(0, 1) → A441
  443. Random(0, 1) → A442
  444. Random(0, 1) → A443
  445. Random(0, 1) → A444
  446. Random(0, 1) → A445
  447. Random(0, 1) → A446
  448. Random(0, 1) → A447
  449. Random(0, 1) → A448
  450. Random(0, 1) → A449
  451. Random(0, 1) → A450
  452. Random(0, 1) → A451
  453. Random(0, 1) → A452
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  456. Random(0, 1) → A455
  457. Random(0, 1) → A456
  458. Random(0, 1) → A457
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  460. Random(0, 1) → A459
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  468. Random(0, 1) → A467
  469. Random(0, 1) → A468
  470. Random(0, 1) → A469
  471. Random(0, 1) → A470
  472. Random(0, 1) → A471
  473. Random(0, 1) → A472
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  477. Random(0, 1) → A476
  478. Random(0, 1) → A477
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  486. Random(0, 1) → A485
  487. Random(0, 1) → A486
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  497. Random(0, 1) → A496
  498. Random(0, 1) → A497
  499. Random(0, 1) → A498
  500. Random(0, 1) → A499
  501. Sequence(Random[0, 1], i, 1, 300, 1) → ListOfCoin
  502. Sequence((i, Sum[ListOfCoin, i] / i), i, 1, 300, 1) → RelFreq
  503. Element(RelFreq, n) → A
  504. Sequence(Sum[ListOfCoin, i], i, 1, 300, 1) → NrOfHead
  505. Element(NrOfHead, n) → noh

AI Drawing Prompt Reference

Create a dynamic chart simulating a coin-tossing experiment, showing how the relative frequency of heads converges to 0.5 as the number of trials increases. Include a slider to adjust the trial count, a horizontal dashed line at y=0.5 representing the theoretical probability, and a line graph that updates with each trial, plotting the cumulative frequency of heads. Use distinct colors for heads and tails outcomes, with the x-axis as trial number and y-axis as relative frequency. The line should visibly stabilize near the reference line as trials grow, illustrating the law of large numbers.
The prompt above was compiled from the original drawing commands and is for reference only.