Probability
Subcategories
Puzzles
- acute.triangleWhat are the odds for a random triangle to have only acute angles? New
- amoebaA jar begins with one amoeba.
- aprioriAn urn contains one hundred white and black balls.
- base.rateAn AIDS test shows the right result 99% of the time. New
- bayesOne urn contains black marbles, and the other contains white or black marbles with even odds.
- bus.packsI often shop downtown in the afternoon, leave at a random time, and take the bus home. New
- cabA cab was involved in a hit and run accident at night. Added material
- cancellationA semi popular system to beat the roulette table is called the cancellation system. New
- chip.gameSue and Bob are playing a game in which Sue starts with A chips, Bob starts with B chips, and they play... New
- chutes.and.laddersWhat is the expected number of moves it takes a single player to win Chutes and Ladders? New
- consecutiveYou have a cube with two sides painted red.
- coprimeWhat's the probability that two positive integers chosen at random will be coprime? New
- couponThere is a free gift in my breakfast cereal. Added material
- dartsPeter throws two darts at a dartboard, aiming for the center.
- derangement12 men leave their hats with the hat check. Added material
- dice.totalsLet f[n,s](x) be the probability of rolling the total x on n fair s-sided dice. New
- die.shuffleYou have just won $6,000,000 at a casino. New, unsolved
- disease.testA rare dread disease strikes one out of a million people at random. New
- distinct.digitsWhat is the expected number of different digits in a random 9-digit string, such as a U.S. New
- dna.matchThe probability that an innocent man would match the DNA found at a crime scene is about one in a million. New
- fair.gameIn this coin game between A and B, who is favored? New
- fair.russian.rouletteHow can you play Russian Roulette with each person having a 50/50 chance of losing?
- familySuppose that it is equally likely for a pregnancy to deliver a baby boy as it is to deliver a baby girl.
- fly.on.clockA fly lands on the face of a clock whose minute hand extends to the edge of the face and whose hour hand is... New
- four.ballsYou have four balls in a bag. New
- friday.13thWhat is the chance of a Friday being the 13th of the month? New
- gerrymanderYou have two urns and 100 marbles, 50 white and 50 black.
- gold.coins.drawersWe have three drawers with coins in them, and we know which drawers have which coins: New
- headlightsAt dusk you want to turn on your headlights when half of the oncoming drivers have theirs on, judging only... New, unsolved
- hit.targetCharlie hits the target 80 times in 100 shots. New
- hospitalA town has two hospitals, one big and one small.
- icosThe "house" rolls two 20-sided dice and the "player" rolls one 20-sided die.
- intervalsGiven two random points x and y on the interval 0..1, what is the average size of the smallest of the three...
- killers.and.pacifistsYou enter a town that has K killers and P pacifists.
- knight.returnA knight starts on square A1 of a chessboard and makes random moves (each legal move equally likely) until it is again on A1. New
- leading.digitWhat is the probability that the ratio of two random reals starts with a 1?
- lightsWaldo and Basil are exactly m blocks west and n blocks north from Central Park, and always go with the...
- lost.in.planeA starship lost 100 light-millennia from Sol knows only its distance from Sol, not the direction; jumping... New
- lotteryThere are n tickets in the lottery, k winners and m allowing you to pick another ticket.
- lottery.consecutiveIn a lottery drawing 6 numbers from 1 to 50, what is the probability that the drawing contains at least one... New
- marble.gameYou start with a box holding one black and one white marble, and sample twice with replacement. New
- marbles.ten.moreIn a vase are 10 more black marbles than white marbles. New, unsolved
- martingaleIn roulette, if you begin by betting one dollar on red, then double your bet if you lose, and double again... Added material
- menagesYou have a dinner-party, with a big, round table in the center of the room. New
- nearest.neighborYou are one of many birds arranged at random along an infinitely long telephone wire. New
- nesting.cupsA two year old has 8 plastic cups of different sizes that can be put inside each other. New
- nine.black.marblesI have a bag that initially held 10 marbles. New
- no.two.meetN people agree to meet between 2:00 and 3:00 P.M. New
- normal.tailHow can one calculate the probability of large random deviates (Z scores), such as 15 sigma from the expected mean? New
- oldest.girlYou meet a stranger on the street, and ask how many children he has. Added material
- ones.in.windowIn a linear string of N elements, each element independently takes the value 1 with probability p and 0 with probability 1-p. New
- particle.in.boxA particle is bouncing randomly in a two-dimensional box.
- pebbles.in.pondYou throw N pebbles into a round pond, uniformly distributed. New
- phone.numbersMy sister was assigned a new 7-digit phone number that differs from mine only in the first and last digits. New
- piAre the digits of pi random (i.e., can you make money betting on them)?
- pi.ninesWhat is the probability that the decimal expansion of pi contains a sequence of exactly one million nines... New
- prefix.overlapConsider an alphabetized list of words which has been compressed by replacing the characters repeated... New
- random.chordA long straw is tossed at random onto a circle; given that it falls so that it intersects the circle, what... New
- random.polygon.centerPoints are chosen uniformly at random on a circle until their convex hull contains the center. New
- random.walkWaldo has lost his car keys!
- randomness.vs.chaosCan one tell true randomness apart from the output of a deterministic (chaotic) system? New
- reactorThere is a reactor in which a reaction is to take place.
- rouletteYou are in a game of Russian roulette, but this time the gun (a 6 shooter revolver) has three bullets... Added material
- same.color.halfA bag holds white and black marbles, with 10 more white than black. New
- set.card.guessDraw a Set card from the deck. New, unsolved
- sex.ratioIs the sex of a baby a fair coin toss, independent from one birth to the next, or can some parents be more... New
- shooting.roomYou are led into a room where everyone will be shot if two dice come up double sixes, but a sign says at... New
- singular.binary.matrixWhat is the probability that a randomly written n x n binary matrix (all elements 1 or 0) is singular? New
- sock.drawerFrom a pile of 25 different pairs of socks, how many socks must you pull out on average before you get a... New
- t.distributionGiven a value t of Student's t statistic, is there an approximation or a fairly straightforward way to... New
- taxisYou are looking for a taxi in a town where all taxis are individually numbered 1,2,3,... New
- tennis.meetingN players are entered in a singles tennis tournament. New
- tennis.serveYou hear on the radio that your favorite tennis player won her latest match 6-4 6-4 without ever having her serve broken. New
- tetragonsPick 4 random points A, B, C, D in a plane (in a rectangle, say) and draw the tetragon A-B-C-D-A. New
- three.antsThree ants are at different corners of a triangle.
- three.boxesThree boxes each contain two coins: two gold (gg), two silver (ss), and one silver, one gold (sg). New
- three.sided.coinIf you toss a coin, it rarely lands on its edge. New
- transitivityCan you number dice so that on average die A beats die B beats die C beats A?
- two.cuts.yield.triangleIf a line is cut in two independent random places, what are the odds that the pieces can form a triangle? Added material
- two.wins.in.a.rowTo win a prize you must win two games of chess in a row out of three, alternating between a strong player... New
- up.down.sequenceAssume all random numbers come from the uniform distribution on the unit interval. New
- updating.meanHow can estimates of the mean and standard deviation of a series of observations be updated in a... New, unsolved
- wine.labelsYou are given 9 unlabeled bottles of wine, all different, and the 9 labels that belong on them, but you don't know which is which. New
- wrong.seat100 passengers board a plane with 100 seats; the first, a crazy old lady, takes a wrong seat, and each... New