Level 1: Basic probability intuition

Sample spaces, counting, complements, symmetry, and independence — the reflexes every desk screen assumes you already have.

36 problems

First 5 free · rest Premium

  1. 1

    Sum of Two Dice

    ●○○○○Warm-up~2 min

  2. 2

    Chevalier de Méré

    ●●○○○Easy~4 min

  3. 3

    Birthday Paradox

    ●●○○○Easy~5 min

  4. 4

    Exactly Two Heads in Three Flips

    ●○○○○Warm-up~2 min

  5. 5

    Drawing Two Aces

    ●●○○○Easy~3 min

  6. 6

    Fair Bit from a Biased Coin

    ●●●○○Medium~6 min

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  7. 7

    A Matching Pair of Socks

    ●●○○○Easy~3 min

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  8. 8

    Three Coins, All Alike

    ●○○○○Warm-up~2 min

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  9. 9

    The Rendezvous

    ●●●○○Medium~6 min

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  10. 10

    Even Product

    ●○○○○Warm-up~2 min

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  11. 11

    Two Cards, Same Colour

    ●●○○○Easy~3 min

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  12. 12

    Is the Second Card More Likely Red?

    ●●○○○Easy~3 min

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  13. 13

    Three Dice Alike

    ●○○○○Warm-up~2 min

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  14. 14

    Is the Sum Even?

    ●○○○○Warm-up~2 min

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  15. 15

    At Least One Six in Three Dice

    ●●○○○Easy~3 min

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  16. 16

    Three Points on a Circle

    ●●●○○Medium~6 min

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  17. 17

    Two Points Far Apart

    ●●○○○Easy~4 min

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  18. 18

    The Extra Coin

    ●●●○○Medium~6 min

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  19. 19

    Does One Die Beat the Other?

    ●○○○○Warm-up~2 min

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  20. 20

    Sampling for Defectives

    ●●○○○Easy~4 min

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  21. 21

    Breaking a Stick into a Triangle

    ●●●○○Medium~6 min

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  22. 22

    Sharing a Birth Month

    ●○○○○Warm-up~3 min

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  23. 23

    Buffon's Needle

    ●●●●○Hard~8 min

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  24. 24

    No Two Heads in a Row

    ●●●○○Medium~6 min

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  25. 25

    Probability of a Flush

    ●●●○○Medium~5 min

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  26. 26

    Sum Divisible by Three

    ●○○○○Warm-up~3 min

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  27. 27

    Seated Together?

    ●●○○○Easy~3 min

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  28. 28

    A Random Palindrome

    ●●○○○Easy~3 min

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  29. 29

    Six Before One

    ●●○○○Easy~3 min

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  30. 30

    Closer to the Centre or the Edge?

    ●●●●○Hard~8 min

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  31. 31

    Probability of Two Pair

    ●●●○○Medium~6 min

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  32. 32

    A Run of k Heads

    ●●●○○Medium~6 min

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  33. 33

    Nobody Gets Their Own

    ●●●○○Medium~6 min

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  34. 34

    Balls in Boxes — Four Ways

    ●●●○○Medium~6 min

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  35. 35

    Consecutive Ranks

    ●●○○○Easy~4 min

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  36. 36

    A Void in Bridge

    ●●●○○Medium~5 min

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