AI Grounds

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Guided discovery

Conditional Probability

Keep the overlap. Change who counts.

A = practiced with feedback

B = passed the check

Choose one of the 100 fictional people at random. Each person is equally likely; changing views never changes their facts.

Your population

✓ marks groups counted in the numerator. Outlined groups are eligible for the denominator; excluded groups say Outside denominator.

100 people, partitioned by their two facts. Row and column labels define each group.
GroupBOutside BTotal
A22✓ Counted18Eligible40
Outside A8Eligible52Eligible60
Total3070100

Selected: A ∩ B = 22/100; 22%

The denominator is all 100 people. The selected view counts 22 of them.

Show all 100 people

A+B means both facts; — means neither. ✓ means counted; × means outside the denominator. Person numbers identify fixed people, not a time sequence.

  1. 1A+B✓
  2. 2A+B✓
  3. 3A+B✓
  4. 4A+B✓
  5. 5—·
  6. 6—·
  7. 7—·
  8. 8—·
  9. 9—·
  10. 10—·
  11. 11A+B✓
  12. 12A+B✓
  13. 13A+B✓
  14. 14A+B✓
  15. 15—·
  16. 16—·
  17. 17—·
  18. 18—·
  19. 19—·
  20. 20—·
  21. 21A+B✓
  22. 22A+B✓
  23. 23A+B✓
  24. 24A+B✓
  25. 25—·
  26. 26—·
  27. 27—·
  28. 28—·
  29. 29—·
  30. 30—·
  31. 31A+B✓
  32. 32A+B✓
  33. 33A+B✓
  34. 34A+B✓
  35. 35—·
  36. 36—·
  37. 37—·
  38. 38—·
  39. 39—·
  40. 40—·
  41. 41A+B✓
  42. 42A+B✓
  43. 43A+B✓
  44. 44A+B✓
  45. 45—·
  46. 46—·
  47. 47—·
  48. 48—·
  49. 49—·
  50. 50—·
  51. 51A+B✓
  52. 52A+B✓
  53. 53A·
  54. 54A·
  55. 55—·
  56. 56—·
  57. 57—·
  58. 58—·
  59. 59—·
  60. 60—·
  61. 61A·
  62. 62A·
  63. 63A·
  64. 64A·
  65. 65—·
  66. 66—·
  67. 67—·
  68. 68—·
  69. 69—·
  70. 70—·
  71. 71A·
  72. 72A·
  73. 73A·
  74. 74A·
  75. 75—·
  76. 76—·
  77. 77—·
  78. 78—·
  79. 79—·
  80. 80—·
  81. 81A·
  82. 82A·
  83. 83A·
  84. 84A·
  85. 85B·
  86. 86B·
  87. 87B·
  88. 88B·
  89. 89—·
  90. 90—·
  91. 91A·
  92. 92A·
  93. 93A·
  94. 94A·
  95. 95B·
  96. 96B·
  97. 97B·
  98. 98B·
  99. 99—·
  100. 100—·

P(B)

Marginal: B out of everyone.

30/100

30%

P(B given A)

Conditional: B only inside A.

—

Choose B given A to compare.

P(A ∩ B)

Joint: both facts out of everyone.

22/100

22%

Does knowing A change the rate of B?

Predict first, then choose B given A to compare the two rates.

These fixed populations show association; they do not establish cause and effect.

Dependent; A ∩ B counts 22 out of 100.