Isaac Newton Helps Samuel Pepys (Problem 18) - Which of three events is more likely when throwing dice?
Trials Until First Success (Problem 4) - On average, how many times must a die be thrown until one rolls a six?
An Even Split at Coin Tossing (Problem 17) - When 100 coins are tossed, what is the probability that exactly 50 are heads?

The First Ace (Problem 40) - How many cards are dealt from a shuffled deck before the first ace appears?
Average Number of Matches (Problem 43) - What is the average number of matches between two decks of shuffled cards?

Chuck-a-Luck (Problem 19) - What is the player's expected loss per unit stake in Chuck-a-Luck?
Craps (Problem 20) - What is the player's chance to win at Craps?
Curing the Compulsive Gambler (Problem 21) - Will a player be behind after 36 plays of one number in Roulette?
Gambler's Ruin (Problem 24) - What is the probability of a player winning under specific conditions?
Bold Play vs. Cautious Play (Problem 25) - Compare the merits of two different gambling strategies.

Lengths of Random Chords (Problem 26) - What is the probability that a random chord on a circle exceeds its radius?
The Clumsy Chemist (Problem 28) - What is the average length of pieces from randomly broken glass rods?
The Little End of the Stick (Problem 30) - What is the average length of the smaller piece of a randomly broken stick?
The Broken Bar (Problem 31) - What are the average sizes of all pieces of a bar randomly broken in three?

Collecting Coupons (Problem 14) - How many coupons must you collect to complete a set?
The Theater Row (Problem 15) - How many adjacent "marriageable couples" are expected in a random row of 15?

Successive Wins (Problem 2) - Which series of games offers a better probability of winning two in a row?
The Flippant Juror (Problem 3) - Which jury has a better probability of making the correct decision?
Catching the Cautious Counterfeiter (Problem 23) - What is the probability of catching a counterfeiter during sampling?
The Hurried Duelers (Problem 27) - If duelists arrive at random times, what fraction of duels lead to violence?
Will Second-Best Be Runner-Up? (Problem 10) - What is the probability that the second-best player is the runner-up in a tournament?
Twin Knights (Problem 11) - What are the odds that twins will meet in a tournament?

Miscellaneous Puzzles

Problems from various sources including FiveThirtyEight, Futility Closet, and Twitter.

The Petersburg Paradox - What would be a fair price to pay the casino for entering the game?
Yahtzee - What is the probability of rolling five of a kind with three rolls?
Carnival Barker - What is the expected value of winnings in a specific carnival dice game?
Three Flips - Should you pay to play a specific coin-flipping game with tiered payouts?
Flipping Four Coins - Evaluating a bet on whether heads and tails both appear twice in four flips.

Coin Flip Sequences - Which sequence takes longer on average: HTH or HTT?
A Dicey Question - Is it more likely to roll exactly one six or no sixes in five dice?
Flipping 100 Coins - How many rounds until only one coin remains when re-flipping heads?
Chance of Dying - What are the chances of rolling a sum of 57 or greater with 19 dice?

All Aboard - What’s the probability that the last passenger on an airplane finds his seat occupied?
Theater Seats - What is the probability that two friends won't sit together in a cinema?
Gummy Bears - What is the probability of selecting five different flavors from a pack?
Infinite Monkeys - Probability of specific names appearing if monkeys type letters at random.
Minority Selection - Probability that no member of a minority party is selected for N slots.
Bags of Marbles - Probability that a second marble drawn is white in a specific game.
A Painting Puzzle - What is the expected number of turns for all balls to become the same color?

Hit and Run - Bayesian probability of a cab's color involved in an accident.
State Names Letter Frequency - Analysis of letter frequencies in US state names.

Lunch in the Park - What is the probability that two friends meet for lunch given random arrivals?
Missiles - Probability that a target is hit by at least one of four missiles.
Quiz Answers - Generating an optimal strategy for a specific quiz game.
Draw Two - Expected value of the sum of two integers drawn from 1-10.
Exceed 1 - How many random numbers are needed to sum to more than 1?
How Long Will You Shuffle This Damn Deck Of Cards - Reversals required in a specific card shuffling problem.
Lonely Card Game - Probability of winning a game where you lose on a rank match during deal.

Probability Puzzles