Level 2: Conditional probability

Bayes' theorem, base rates, and updating on evidence — where intuition fails most reliably and interviewers probe hardest.

36 problems

First 5 free · rest Premium

  1. 1

    The Monty Hall Problem

    ●●●○○Medium~5 min

  2. 2

    The Two-Children Problem

    ●●●○○Medium~5 min

  3. 3

    False Positives and Base Rates

    ●●●○○Medium~5 min

  4. 4

    Which Coin Did I Flip?

    ●●○○○Easy~4 min

  5. 5

    The Blue-Cab Problem

    ●●●○○Medium~5 min

  6. 6

    The Three Prisoners

    ●●●●○Hard~7 min

    Premium
  7. 7

    Bertrand's Box Paradox

    ●●●○○Medium~5 min

    Premium
  8. 8

    The Prosecutor's Fallacy

    ●●●○○Medium~6 min

    Premium
  9. 9

    Simpson's Paradox

    ●●●●○Hard~7 min

    Premium
  10. 10

    The Tuesday Boy

    ●●●●○Hard~7 min

    Premium
  11. 11

    Monty Hall with 100 Doors

    ●●○○○Easy~4 min

    Premium
  12. 12

    Aces: 'At Least One' vs 'The Ace of Spades'

    ●●●●○Hard~7 min

    Premium
  13. 13

    Laplace's Rule of Succession

    ●●●●○Hard~7 min

    Premium
  14. 14

    Monty Hall with a Clueless Host

    ●●●○○Medium~5 min

    Premium
  15. 15

    Which Urn Did the Ball Come From?

    ●●●○○Medium~5 min

    Premium
  16. 16

    Two Positive Tests

    ●●●○○Medium~6 min

    Premium
  17. 17

    The Pólya Urn

    ●●●●○Hard~7 min

    Premium
  18. 18

    The Conjunction Fallacy

    ●●○○○Easy~4 min

    Premium
  19. 19

    The Two-Envelope Paradox

    ●●●●○Hard~7 min

    Premium
  20. 20

    Monty Hall with a Biased Host

    ●●●●○Hard~7 min

    Premium
  21. 21

    Conditioning on a Region

    ●●●○○Medium~5 min

    Premium
  22. 22

    Carrier Probability

    ●●●○○Medium~5 min

    Premium
  23. 23

    The Coin Has No Memory

    ●●○○○Easy~4 min

    Premium
  24. 24

    The Lost Boarding Pass

    ●●●●○Hard~8 min

    Premium
  25. 25

    Which Flip Was the Head?

    ●●○○○Easy~3 min

    Premium
  26. 26

    Transfer Then Draw

    ●●●●○Hard~6 min

    Premium
  27. 27

    Fair, Two-Headed, or Two-Tailed?

    ●●●○○Medium~5 min

    Premium
  28. 28

    Which Machine Made the Defect?

    ●●●○○Medium~5 min

    Premium
  29. 29

    How Reassuring Is a Negative?

    ●●●○○Medium~5 min

    Premium
  30. 30

    The Multiple-Testing Trap

    ●●●○○Medium~6 min

    Premium
  31. 31

    I Met One of His Children

    ●●●○○Medium~6 min

    Premium
  32. 32

    Bertrand's Chord Paradox

    ●●●●○Hard~7 min

    Premium
  33. 33

    Expectation Given a Threshold

    ●●●○○Medium~5 min

    Premium
  34. 34

    Splitting a Poisson Total

    ●●●●○Hard~6 min

    Premium
  35. 35

    Fair or Biased After a Sequence?

    ●●●○○Medium~5 min

    Premium
  36. 36

    Cold Hit vs Probable Cause

    ●●●●○Hard~7 min

    Premium