Back to all courses

Perplexing Probability

Warp your brain with these tricky probability puzzles.

Probability is full of counter-intuitive results and paradoxes.

Challenge yourself by learning how to mathematically master some very surprising games and experiments including the Monty Hall game show, the Boy or Girl paradox, and the Tuesday paradox.

Interactive
quizzes

19

Concepts and
exercises

110+
  1. 1

    Introduction

    Don't expect to get all of these questions correct – some of them initially stump almost everyone.

    1. Gaming Strategies

      Learn some quick "pro tips" for solving probability puzzles.

    2. Probability is Everywhere

      Discover some counter-intuitive results when you applying probability to these real-life scenarios!

    3. Exposing Misconceptions

      Challenge yourself with probability puzzles that trip up plenty of experts.

  2. 2

    Survive This Chapter

    Dodge death by poison, Russian roulette, and a crazy prison warden.

    1. Included with
      Brilliant Premium

      Poisoned Fruit

      Get started with dependent probability ... and avoid the poison!

    2. Included with
      Brilliant Premium

      The Crazy Warden

      Outwit the warden and try to survive.

    3. Included with
      Brilliant Premium

      Russian Roulette

      Tricky conditions can make survival hard to calculate.

    4. Included with
      Brilliant Premium

      Spin or Shoot?

      Should you try your luck or spin first?

  3. 3

    Brain-Warping Probability

    Most people's intuitions about the odds of winning these games are wrong.

    1. Included with
      Brilliant Premium

      The Monty Hall Game

      The famous mind-bender: find the car and avoid the man-eating goat!

    2. Included with
      Brilliant Premium

      More Man-Eating Goats

      What happens when Monty Hall has a lot more doors?

    3. Included with
      Brilliant Premium

      The Boy-or-Girl Paradox

      A small change of conditions can make a big difference.

    4. Included with
      Brilliant Premium

      Tuesday Changes Everything

      Explore this counterintuitive twist to the Boy-or-Girl Paradox.

  4. 4

    Crazy Mad Dice

    Custom crafted competitive craziness.

    1. Included with
      Brilliant Premium

      Crazy Dice Warmup

      See what happens when the dice don't read 1 to 6 anymore.

    2. Included with
      Brilliant Premium

      Competitive Design

      Design your own dice and try to beat your friends.

    3. Included with
      Brilliant Premium

      Beating a Standard Die (I)

      Under what conditions can you beat a regular die?

    4. Included with
      Brilliant Premium

      Beating a Standard Die (II)

      Explore more scenarios that match a custom die against a standard one.