Probability & Stats Problems

486 worked problems drawn from published quant interview prep material, each with a full step-by-step solution. Sign in to submit answers and track your progress.

• 01Grid Paths on a 6×6 Boardcombinatorics★★★
• 02A Frog That Won't Repeat Itselfcombinatorics★★★
• 03Avoiding the Digit Sixcombinatorics★★★
• 04Even, Odd, Then Differentclassical probability★★★
• 05A Sixty-Four-Sided Die With a Feeoptimal stopping★★★
• 06Bus on a Ten-Minute Loopexpected value★★★
• 07Twenty Up, Five Downexpected value★★★
• 08Smallest Card Beside the Hundredexpected value★★★
• 09Expectation of a Lognormalclassical probability★★★
• 10The Dealer's Fair Priceexpected value★★★
• 11Adjacent Bulletsconditional probability★★★
• 12Rock, Paper, No Rockexpected value★★★
• 13A Dollar a Headexpected value★★★
• 14Two Dice Summing to 6classical probability★★★
• 15Two Thirds Off the Buspuzzles★★★
• 16Digits in 100 Factorialpuzzles★★★
• 17Longest Piece of a Broken Stickgeometric probability★★★
• 18Two Primes With an Even Sumcombinatorics★★★
• 19Three-Card Straight from 8 Decksclassical probability★★★
• 20Fixing Your Number in the Pairs Gameexpected value★★★
• 21One Coin Backexpected value★★★
• 22Do the Segments Overlapgeometric probability★★★
• 23Five Tyres, Three Wheelspuzzles★★★
• 24All Heads, Given at Least Oneconditional probability★★★
• 25At Most Two Tails in Fivecombinatorics★★★
• 26The Bus That Stops for Ice Creamexpected value★★★
• 27No Car for Fifteen Minutesconditional probability★★★
• 28Two Dice Summing to 8classical probability★★★
• 29Minimum Odds to Callexpected value★★★
• 30When to Stop Drawingoptimal stopping★★★
• 31Two of the Same Colourclassical probability★★★
• 32Never a Six in Ten Rollsclassical probability★★★
• 33More Than Sixty Headscombinatorics★★★
• 34Hearts Count Doubleexpected value★★★
• 35The Better of Two Ratiosexpected value★★★
• 36Five in the Same Monthcombinatorics★★★
• 37A Hundred Cards Against a Guesserexpected value★★★
• 38Four Dice Summing to 20classical probability★★★
• 39A Probably Fake Paintingexpected value★★★
• 40Twenty Horses, Five Lanespuzzles★★★
• 41De Méré's Two Betsclassical probability★★★
• 42No Cup on Its Own Saucercombinatorics★★★
• 43Digit Sum to a Millioncombinatorics★★★
• 44Painting a 10x10x10 Cubecombinatorics★★★
• 45Which Draw Is Largerclassical probability★★★
• 46Two Customers, One Databaseclassical probability★★★
• 47Two Reds From a Double Packclassical probability★★★
• 48A Die With Two Optional Rerollsoptimal stopping★★★
• 49Beating a Sevenclassical probability★★★
• 50Ten-Sided Beats Twenty-Sidedclassical probability★★★
• 51Four of the First Fifteen Primescombinatorics★★★
• 52Counting the Digit 9 up to 1000combinatorics★★★
• 53Sum of Three Cardsexpected value★★★
• 54Finding Just the Fastest Horsepuzzles★★★
• 55Rolling to Three Hundredrandom walks★★★
• 56Beating an Eightclassical probability★★★
• 57Tails Before Two Headsexpected value★★★
• 58Apples to Orlandopuzzles★★★
• 59Product of Two Different Diceexpected value★★★
• 60±1 Walk Ending at 4combinatorics★★★
• 61Two Hundred Coins in a Boxexpected value★★★
• 62Where the Heaviest Weight Sitsclassical probability★★★
• 63Two Workers on One Jobpuzzles★★★
• 64Three Planets Alignedpuzzles★★★
• 65One Coin in a Thousandconditional probability★★★
• 66Clock Hands at 12:15puzzles★★★
• 67Four Planes Through Spacepuzzles★★★
• 68Ten Chips Into Pilespuzzles★★★
• 69One Number Is the Averagecombinatorics★★★
• 70A Bigger Steel Ballpuzzles★★★
• 71Digits in 99 to the Tenthpuzzles★★★
• 72Binary Strings: Start 1 or End 00combinatorics★★★
• 73Mean of the Digit Permutationscombinatorics★★★
• 74The Most Likely Odd Totalrandom walks★★★
• 75Random Walk on a Cuberandom walks★★★
• 76Flips to See HHTmarkov chains★★★
• 77Guessing Four of Fivecombinatorics★★★
• 78Reaching Game Sevenclassical probability★★★
• 79Sum of Three Diceexpected value★★★
• 80Rolling Two Sixesclassical probability★★★
• 81Six Dice, Even Totalclassical probability★★★
• 82Roll Until a Six Ruins Youoptimal stopping★★★
• 83A Square Productcombinatorics★★★
• 84Seven Wins, Even Losesexpected value★★★
• 85Eight-Sided, Then Twelve-Sidedoptimal stopping★★★
• 86Wide Normal Against Narrowclassical probability★★★
• 87A Head Start on the Pondpuzzles★★★
• 88Last Digit of 3 to the 33puzzles★★★
• 89Subsets with Bold Elementscombinatorics★★★
• 90Breaking the Longer Piecegeometric probability★★★
• 91Which Coin Landed Headsconditional probability★★★
• 92Heads a Multiple of Threecombinatorics★★★
• 93Five Digits Multiplying to 120puzzles★★★
• 94HHT Before THHmarkov chains★★★
• 95A Six-by-Six of Plus and Minus Onecombinatorics★★★
• 96At Least One Sixclassical probability★★★
• 97X Against Five Yclassical probability★★★
• 98Casino Triple Matchclassical probability★★★
• 99Exactly Four Heads in Ninecombinatorics★★★
• 100A Cube With No Paint Showingclassical probability★★★
• 101One Giant Loop of Spaghetticlassical probability★★★
• 102Local Minima Around a Circleexpected value★★★
• 103My Twenty Against Their Thirtyexpected value★★★
• 104How Low Can the Correlation Gocorrelation★★★
• 105The Cloning Robotmarkov chains★★★
• 106Working Back to Saturdayclassical probability★★★
• 107Age Order at a Round Tableclassical probability★★★
• 108Waiting for the First Headexpected value★★★
• 109Second Black on the Third Drawcombinatorics★★★
• 110Best Bid on Two Diceexpected value★★★
• 111Socks Until a Pairexpected value★★★
• 112Meeting at the Stationgeometric probability★★★
• 113Painting a 4x4x4 Cubecombinatorics★★★
• 114Hands Coinciding After Threepuzzles★★★
• 115Sum Without Sevens or Eightscombinatorics★★★
• 116Primes in Six Drawsexpected value★★★
• 117A Sum of Sevenclassical probability★★★
• 118Every Even Before Any Oddclassical probability★★★
• 119Ten Bulbs, No Two Adjacentcombinatorics★★★
• 120Re-toss Any Subsetexpected value★★★
• 121Random Tic-Tac-Toecombinatorics★★★
• 122Two Heads in a Rowexpected value★★★
• 123Three Dice Against a Twentyclassical probability★★★
• 124Four Coins With a Costly Re-Tossoptimal stopping★★★
• 125Digits Multiplying to Ten Thousandpuzzles★★★
• 126A Knight After Ten Movescombinatorics★★★
• 127Two Dice, Same Colourclassical probability★★★
• 128Charlie Between Two Boysclassical probability★★★
• 129Twenty Rolls of a Hundred-Sided Dieexpected value★★★
• 130Three Bowlsconditional probability★★★
• 131Three of the First Nine Primescombinatorics★★★
• 132Second Roll or Bust at Thirteenoptimal stopping★★★
• 133How Long Would C Takepuzzles★★★
• 134Every Face at Least Twiceexpected value★★★
• 135Where You Stop Past Thirteenrandom walks★★★
• 136Sharpe of a Biased Coincorrelation★★★
• 137Doors You Can Openexpected value★★★
• 138Variance of a Die Rollcorrelation★★★
• 139A Weighted Hockey-Stick Sumcombinatorics★★★
• 140When Was the Jar Half Fullpuzzles★★★
• 141Tennis From Thirty Allmarkov chains★★★
• 142Heads Times Tailsexpected value★★★
• 143Cards for All Four Suitsexpected value★★★
• 144Largest Pairwise-Coprime Sumpuzzles★★★
• 145Only Zeros and Onespuzzles★★★
• 146Rearranging a Factorisationpuzzles★★★
• 147Clock Hands at 10:45puzzles★★★
• 148Absolute Difference of Two 30-Sided Diceexpected value★★★
• 149Flips to See Two Headsexpected value★★★
• 150Seventeen Coins Against Sixteenclassical probability★★★
• 151Best of Ten Lottery Slotsexpected value★★★
• 152Paid the Sum Unless You Roll Doublesexpected value★★★
• 153Pair-Flip Coin Gameexpected value★★★
• 154Doubling on a Head Streakexpected value★★★
• 155The Coin With Two Headsconditional probability★★★
• 156The First Die Is a Sixconditional probability★★★
• 157Running Off the Bridgepuzzles★★★
• 158Exactly Three Heads in Fivecombinatorics★★★
• 159At Least Four Heads in Sevencombinatorics★★★
• 160Expected Pairs in Five Cardsexpected value★★★
• 161Thirty-Two for Five Headsexpected value★★★
• 162HH Before THmarkov chains★★★
• 163Handshakes Among Four Couplescombinatorics★★★
• 164Three Coins, One Face Showingconditional probability★★★
• 165One Hundred Bottlespuzzles★★★
• 166Flips Until Three Alikeexpected value★★★
• 167Red, Green, Blue at a Cornerclassical probability★★★
• 168Eight Balls, One Heavypuzzles★★★
• 169Two Torpedoesclassical probability★★★
• 170Copy, Paste, Typepuzzles★★★
• 171Another Heartconditional probability★★★
• 172Median of Three Diceexpected value★★★
• 173Weighing Five Melonspuzzles★★★
• 174At Most Two Heads in Fourcombinatorics★★★
• 175Apples Across the Desertpuzzles★★★
• 176Two Balls, Two Whitesconditional probability★★★
• 177Keep the Better of Two Rollsexpected value★★★
• 178Digits Multiplying to 96puzzles★★★
• 179Arranging Colored Balls in a Linecombinatorics★★★
• 180Draw Again or Keepoptimal stopping★★★
• 181The Drunk Passengerconditional probability★★★
• 182Matching Socks from a Drawerclassical probability★★★
• 183A Square Totalcombinatorics★★★
• 184Square of a Die Rollexpected value★★★
• 185At Least Two Heads in Fivecombinatorics★★★
• 186Clock Hands at 9:40puzzles★★★
• 187Truck Within Five Minutesconditional probability★★★
• 188Back to Evenclassical probability★★★
• 189A Hundred-Storey House of Cardspuzzles★★★
• 190Twenty or Five Hundredexpected value★★★
• 191Given One Is Headsconditional probability★★★
• 192Two Reds From the Bagclassical probability★★★
• 193Average Seven-Digit Palindromecombinatorics★★★
• 194Lattice Paths in 3Dcombinatorics★★★
• 195The Fifth Fishconditional probability★★★
• 196Exactly Three Alikecombinatorics★★★
• 197One Coin Against Tworandom walks★★★
• 198Which Urn Gave the Tenconditional probability★★★
• 199Tosses for Four Tailscombinatorics★★★
• 200Passing a Hundred With a Four-Sided Dierandom walks★★★
• 201Fourth Green on the Ninth Drawcombinatorics★★★
• 202Two Tens Off the Topclassical probability★★★
• 203First Tail Takes Itclassical probability★★★
• 204Twenty Up or Ten Downrandom walks★★★
• 205Five Pirates and the Goldpuzzles★★★
• 206Two Painterspuzzles★★★
• 207Three Positive Integers Summing to 25combinatorics★★★
• 208The Largest Unreachable Totalpuzzles★★★
• 209Handshakes Among Four Couplescombinatorics★★★
• 210At Least One Head in Fourclassical probability★★★
• 211Chickens and Eggspuzzles★★★
• 212Largest Unmakeable Postagepuzzles★★★
• 213HTT Before TTHmarkov chains★★★
• 214Eighteen Balls, One Heavypuzzles★★★
• 215Full House in Five Cardscombinatorics★★★
• 216More Than Half Headscombinatorics★★★
• 217Bank Before You Bustoptimal stopping★★★
• 218Handshakes Among Tencombinatorics★★★
• 219Packing 3-Cubes into a 20-Cubecombinatorics★★★
• 220An Even Productclassical probability★★★
• 221Gambler's Ruin With an Edgerandom walks★★★
• 222Tosses Until HHT or HTHmarkov chains★★★
• 223Draws to the First Aceexpected value★★★
• 224Matching Four Coins Eachexpected value★★★
• 225Sum Given at Least One Sixconditional probability★★★
• 226Two Heads With a Biased Coinexpected value★★★
• 227Exactly Fifty Headscombinatorics★★★
• 228Exactly Two Heads in Fourcombinatorics★★★
• 229Ten Heads in a Rowclassical probability★★★
• 230HHT Before HTHmarkov chains★★★
• 231Three Dice Summing to Tencombinatorics★★★
• 232Products Ending in 1, 3, 7, or 9classical probability★★★
• 233Valuing the Propertyexpected value★★★
• 234A Triangle Around the Centregeometric probability★★★
• 235Meteor in Half an Hourconditional probability★★★
• 236Smallest Roll Before a Fiveexpected value★★★
• 237Square of the Headsexpected value★★★
• 238HT Before TTmarkov chains★★★
• 239Exactly Two Aces in 13 Cardsclassical probability★★★
• 240HHT Before HTTmarkov chains★★★
• 241Three Tails, Given Twoconditional probability★★★
• 242Shared Birthday Among Thirtyclassical probability★★★
• 243Sevens Below a Billioncombinatorics★★★
• 244Two Bowling Ballspuzzles★★★
• 245How Correlated Can B and C Becorrelation★★★
• 246Matching Heads With Four Coinscombinatorics★★★
• 247Ruined on Schedulerandom walks★★★
• 248Painting Balls Until They Matchmarkov chains★★★
• 249Flipping Two Balls at a Timemarkov chains★★★
• 250Ten More Heads Than Tailscombinatorics★★★
• 251Squash at Deucemarkov chains★★★
• 252Twelve-Sided or Two Sixesoptimal stopping★★★
• 253Eleven-Sided Plus Seven-Sidedexpected value★★★
• 254HHH Before HTHmarkov chains★★★
• 255Heavy Smoker, Given Deathconditional probability★★★
• 256Three Heads in a Rowcombinatorics★★★
• 257The Minimum of x to the xpuzzles★★★
• 258Six Consecutive Threesclassical probability★★★
• 259Numbers Containing a Zerocombinatorics★★★
• 260The Ballot Problemrandom walks★★★
• 261Six of the First Twelve Primescombinatorics★★★
• 262A Die With One Rerolloptimal stopping★★★
• 263Apples to Londonpuzzles★★★
• 264Rolls to the First Sixexpected value★★★
• 265Meeting in the Finalclassical probability★★★
• 266Seated Next to Your Friendcombinatorics★★★
• 267Twenty as a Sum of Primescombinatorics★★★
• 268At Least Two Heads in Threecombinatorics★★★
• 269Twenty-Five Horsespuzzles★★★
• 270The Smaller of Two Diceexpected value★★★
• 271Counting the Digit Twocombinatorics★★★
• 272Three Balls on a Gridcombinatorics★★★
• 273Clock Hands at 3:15puzzles★★★
• 274Variance of a Hundred Flipscorrelation★★★
• 275An Infinite Power Towerpuzzles★★★
• 276How Many Uniforms to Pass Oneexpected value★★★
• 277Race to First Headsclassical probability★★★
• 278A Positive Test for a Rare Diseaseconditional probability★★★
• 279Reroll One of Two Diceoptimal stopping★★★
• 280A Triangle With Perimeter Fortypuzzles★★★
• 281Five Coins, One Double-Headedconditional probability★★★
• 282Mickey and Minniegeometric probability★★★
• 283A Thousand Doorscombinatorics★★★
• 284First to Two Headsmarkov chains★★★
• 285Second Die Beats the Firstclassical probability★★★
• 286Arranging Coloured Ballscombinatorics★★★
• 287Three Dice in Increasing Orderclassical probability★★★
• 288Monty Hallconditional probability★★★
• 289Even Heads With One Fair Coinclassical probability★★★
• 290A Thousand Bottles, One Poisonedpuzzles★★★
• 291Four-Sided or Six-Sidedconditional probability★★★
• 292Rolls to See Every Faceexpected value★★★
• 293Six Before Fiveconditional probability★★★
• 294Loops From a Hundred Noodlesexpected value★★★
• 295Expected Value of One Dieexpected value★★★
• 296Three Heads in a Rowexpected value★★★
• 297Two Sixes in a Rowexpected value★★★
• 298Cube of a Die Rollexpected value★★★
• 299Neighboring Rollsmarkov chains★★★
• 300Sixteen Watermelonspuzzles★★★
• 301Which Coin After Three Headsconditional probability★★★
• 302Two Diamonds and One Othercombinatorics★★★
• 303Just Past Seventy Thousandpuzzles★★★
• 304An Odd Number of Headsclassical probability★★★
• 305Average Chord Lengthgeometric probability★★★
• 306Consecutive Onescombinatorics★★★
• 307The Throw That Passes a Hundredrandom walks★★★
• 308Expected Distance Across a Circlegeometric probability★★★
• 309Marbles in Two Bagsclassical probability★★★
• 310Five Friends in Age Ordercombinatorics★★★
• 311Rain Over the Weekendclassical probability★★★
• 312Paying With a Gold Barpuzzles★★★
• 313Two Eggs, One Hundred Floorspuzzles★★★
• 314Ramen Noodle Loopsexpected value★★★
• 315Both Sixes, Given One Sixconditional probability★★★
• 316Spotted at the Gymconditional probability★★★
• 317Uniform Sums Past ln 2expected value★★★
• 318Matching Head Countscombinatorics★★★
• 319Variance on a Circlegeometric probability★★★
• 320Which Die Am I Holdingconditional probability★★★
• 321Expected Heads Given at Least Twoconditional probability★★★
• 322The Next Overlap After Noonpuzzles★★★
• 323Swap or Keep Your Numberoptimal stopping★★★
• 324Variance on a Spheregeometric probability★★★
• 325A Beats B Beats Cclassical probability★★★
• 326Roll-or-Take on a d20optimal stopping★★★
• 327Paying for an Eleven or Twelveexpected value★★★
• 328Y Beats Three Xclassical probability★★★
• 329Robot on the Tablerandom walks★★★
• 330Three Quarters Off the Buspuzzles★★★
• 331Y Beats Three X, Given X Positiveconditional probability★★★
• 332Three Coins, All Headsclassical probability★★★
• 333Three Heads or Three Tailsmarkov chains★★★
• 334Trailing Zeros of 100!combinatorics★★★
• 335Shortest Piece of a Broken Stickgeometric probability★★★
• 336Dollar Re-Rollsoptimal stopping★★★
• 337Three Equally Correlated Variablescorrelation★★★
• 338A Hundred-Sided Die With Costly Rerollsoptimal stopping★★★
• 339Penney's Game: HTH vs HHTmarkov chains★★★
• 340Ten Dollars for Four Headsexpected value★★★
• 341Smallest of Three Drawsclassical probability★★★
• 342Corner of a Painted Cubeconditional probability★★★
• 343Ant on a Cubemarkov chains★★★
• 344Sum of the Odd Numberspuzzles★★★
• 345The Limit of x to the xpuzzles★★★
• 346Clock Hands at 2:30puzzles★★★
• 347Best of Two Tossesexpected value★★★
• 348First Aceexpected value★★★
• 349A Seven Somewherecombinatorics★★★
• 350Six Sixes in a Rowexpected value★★★
• 351Crossing Chordsexpected value★★★
• 352Collecting All Four Suitsexpected value★★★
• 353Bidding for the Caroptimal stopping★★★
• 354Risky Second Rolloptimal stopping★★★
• 355The Hidden Faceconditional probability★★★
• 356Last Number Standingpuzzles★★★
• 357A Fibonacci Telescopecombinatorics★★★
• 358First Roll Lowerclassical probability★★★
• 359LOLLIPOP, Bookendedcombinatorics★★★
• 360Another Matching Pairclassical probability★★★
• 361The Heaviest Weight's Sideclassical probability★★★
• 362Tower of 1s and 2scombinatorics★★★
• 363The Third Shiny Pennyclassical probability★★★
• 364Before the Two of Heartsclassical probability★★★
• 365Exactly One Consecutive Paircombinatorics★★★
• 366Turtle Rendezvousrandom walks★★★
• 367The Cashier's Changerandom walks★★★
• 368An Ace for Everyoneclassical probability★★★
• 369The Last Cherryclassical probability★★★
• 370Boy–Girl Neighborsexpected value★★★
• 371Tails Come in Pairscombinatorics★★★
• 372Labeling a Blank Diecombinatorics★★★
• 373The Missing Sevenclassical probability★★★
• 374Non-Decreasing Codescombinatorics★★★
• 375Ten Lines, Many Regionscombinatorics★★★
• 376Exactly One Pairclassical probability★★★
• 377Sum of 4 Before Sum of 2classical probability★★★
• 378Median of Three Uniformsclassical probability★★★
• 379Three Ants on a Triangleclassical probability★★★
• 380Did Gabe Know It?conditional probability★★★
• 381Coin-Flip Bankruptcyrandom walks★★★
• 382Alternating Die Duelmarkov chains★★★
• 383Convincingly Double-Headedconditional probability★★★
• 384Six Heads from a Random Coinconditional probability★★★
• 385Bertrand's Bowlsconditional probability★★★
• 386An Even Number of Flipsclassical probability★★★
• 387One Extra Coinclassical probability★★★
• 388Fair Meets Loadedclassical probability★★★
• 389One Specific Sequenceconditional probability★★★
• 390Independent Family Eventsconditional probability★★★
• 391The Witness Problemconditional probability★★★
• 392Trapped Behind Five Doorsexpected value★★★
• 393Divisors of a Googol-ish Numberclassical probability★★★
• 394Poisson Coin, No Headsclassical probability★★★
• 395The Hundredth Coinconditional probability★★★
• 396The Added Babyconditional probability★★★
• 397Uncorrelated but Dependentcorrelation★★★
• 398Origin in the Middlegeometric probability★★★
• 399Where the Maximum Landsclassical probability★★★
• 400Biggest of Fourclassical probability★★★
• 401A Product Above One-Halfgeometric probability★★★
• 402The Broken Stickgeometric probability★★★
• 403Will the Table Stand?geometric probability★★★
• 404Min Plus Maxclassical probability★★★
• 405Same Binary Magnitudeclassical probability★★★
• 406Overlapping Segmentsgeometric probability★★★
• 407Conditioned on the Radiusexpected value★★★
• 408Sum Versus Gapgeometric probability★★★
• 409Rolling to an Even Sumexpected value★★★
• 410The Fair Value of Ignoring Onesexpected value★★★
• 411Correlation Through a Shared Termcorrelation★★★
• 412Walking the Circle to Zerorandom walks★★★
• 413Four Jacks in a Rowexpected value★★★
• 414Sum and Difference, Perfectly Correlatedcorrelation★★★
• 415Fixed Points of a Random Functionclassical probability★★★
• 416The Cheapest MGFexpected value★★★
• 417Expected Gap of Two d30sexpected value★★★
• 418Guess the Ball, Get the Countexpected value★★★
• 419Waiting for a Big Bidexpected value★★★
• 420Counting Runsexpected value★★★
• 421Ten Up or Seven Downrandom walks★★★
• 422Reunited Couplesexpected value★★★
• 423Average Dart Distancegeometric probability★★★
• 424Opposite Endsexpected value★★★
• 425One Redraw Allowedoptimal stopping★★★
• 426Rolling Until It's Matchedexpected value★★★
• 427The Middle Dieexpected value★★★
• 428Minimum-Variance Blendcorrelation★★★
• 429A Random Antisymmetric Determinantexpected value★★★
• 430One Re-Flip Eachoptimal stopping★★★
• 431Turning the Basket Blueexpected value★★★
• 432The Winner's Curseoptimal stopping★★★
• 433Two Sixes in a Rowexpected value★★★
• 434Push Your Luck on a d10optimal stopping★★★
• 435The Wait That Never Averagesexpected value★★★
• 436All Six Facesexpected value★★★
• 437Coin on the Chessboardgeometric probability★★★
• 438One Fair Coin Saves Parityclassical probability★★★
• 439Rigging the Candy Boxesconditional probability★★★
• 440Rain Without Independenceclassical probability★★★
• 441Air and Water Before Fireclassical probability★★★
• 442Five Before Snake Eyesconditional probability★★★
• 443A Random Subset of a Random Subsetcombinatorics★★★
• 444The Twice-Red Painted Cubeconditional probability★★★
• 445Positive Given a Positive Sumconditional probability★★★
• 446Three Chords, No Crossingscombinatorics★★★
• 447The German Tank Problemestimation★★★
• 448Russian Roulette, No Re-Spinclassical probability★★★
• 449Whisper Down the Lanemarkov chains★★★
• 450Waiting for Heads-Headsexpected value★★★
• 451Letters to the Wrong Firmsexpected value★★★
• 452Uniform Sum Past Twoexpected value★★★
• 453Fives Before the First Sixexpected value★★★
• 454Waiting for H-T-Hexpected value★★★
• 455The Last Bulb Standingexpected value★★★
• 456Variance of the Longer Pieceexpected value★★★
• 457Crashes on the Half Hourclassical probability★★★
• 458The Dented Dieclassical probability★★★
• 459Pair on Topclassical probability★★★
• 460Four Primes, Even Sumcombinatorics★★★
• 461Position in the Sundae Linecombinatorics★★★
• 462Penalty Kicks and Pólya's Urnconditional probability★★★
• 463Beat the Dealer's Cardclassical probability★★★
• 464All Lines Oddcombinatorics★★★
• 465One Bulb Against Tenclassical probability★★★
• 466A Small Triangle Somewheregeometric probability★★★
• 467Seven Bills from Eightexpected value★★★
• 468A Call Option on Two Diceexpected value★★★
• 469Half the Sum, Exactlyexpected value★★★
• 470One Extra Roll for Primesclassical probability★★★
• 471Visible Heads in a Lineexpected value★★★
• 472Long Cycles in a Random Permutationexpected value★★★
• 473Local Maxima in a Random Line-Upexpected value★★★
• 474Redraws at Two Centsoptimal stopping★★★
• 475When the Sequence Stops Fallingexpected value★★★
• 476Fair Price per Doorexpected value★★★
• 477Three Geometrics in Strict Orderclassical probability★★★
• 478Laplace Transform of an Exit Timebrownian motion★★★
• 479The Frog's Favorite Numberrandom walks★★★
• 480Halving Coins to a Perfect Finishclassical probability★★★
• 481Race to Three of a Kindexpected value★★★
• 482The Arc That Catches the Pointgeometric probability★★★
• 483Maximum Variance on an Intervalexpected value★★★
• 484Overlap of Two Random Subsetsexpected value★★★
• 485Closed Groups at the Partyexpected value★★★
• 486Pricing a Straddle at Zeroexpected value★★★