絞り込み結果
16 件並び順
11:41ENFive Ways to Calculate the Wait for a Successful ShotSawyer · Jane StreetA 20% success rate leads to an expected wait of five attempts—but two consecutive successes take 30. Explore the reasoning through series, recursion and a long-run argument.
10:32ENReal Numbers: Expected Time Between Exams and a Half-Court Shot ChallengeSawyer · Jane StreetSawyer solves an exam-scheduling problem in several ways, then asks how many basketball attempts it takes to make one shot or two in a row.
6:04ENFinals Week and the Expected Number of Snowboards UsedSawyer · Jane StreetSawyer poses a new exam-scheduling puzzle and uses indicator variables in two ways to solve the previous snowboard problem.
6:16ENIndicator Variables: Marching Bands and SnowboardsSawyer · Jane StreetSawyer uses linearity of expectation to count in-step rows, then poses a six-snowboard challenge.
9:40ENReal Numbers: A Marching Band Challenge, Expected Damage, and Bayes’ RuleSawyer · Jane StreetSawyer introduces a marching-band expected-value puzzle and uses linearity and Bayesian updating to solve a monster-attack problem.
10:08ENExpected Damage and a Golden-Ratio Window PuzzleSawyer · Jane StreetSawyer introduces expected value with an unknown video-game monster, then uses geometry to solve a painting-through-a-window problem.
7:55ENThe Art Thief’s Window and a Toy Boat’s Return JourneySawyer · Jane StreetSawyer poses a geometric window puzzle and solves the previous episode’s river-crossing problem in two ways.
5:38ENWavey’s Return: Solving a River-Crossing PuzzleSawyer · Jane StreetSawyer solves the first toy-boat crossing with a 5:3 speed ratio, then asks how the answer changes when the return journey starts 60 meters downstream.
6:37ENCrossing the River: A Toy Boat Puzzle and a Snow-Cone SolutionSawyer · Jane StreetA toy boat drifts downstream in a steady current. Sawyer poses a navigation puzzle and solves the previous episode’s cone-and-hemisphere problem.
3:35ENSnow Cones and Spheres: A Volume Solution and a New Geometry PuzzleSawyer · Jane StreetSawyer derives the height of a cone with the same volume as a hemisphere, then asks how to reshape the ice with minimal movement.
5:39ENA Snow Cone Geometry Puzzle and a Piggy Bank ProbabilitySawyer · Jane StreetSawyer poses a cone-design challenge and solves a conditional probability problem in two ways.
7:03ENGrandma’s Secret College Fund: A Bayes’ Theorem PuzzleSawyer · Jane StreetA random $20 bill reveals information about a hidden deposit. Sawyer poses the new puzzle and solves a DMV probability problem three ways.
7:23ENBayes' Theorem and a Driver's Test Probability PuzzleSawyer · Jane StreetSawyer derives Bayes' theorem, poses a question about test-takers who studied, and solves an earlier card-game probability puzzle.
8:03ENReal Numbers: A Taxi Challenge and Two Ways to Calculate a Sleep ProbabilitySawyer · Jane StreetSawyer poses a consecutive-taxi puzzle and solves a five-night dog-sitting problem with a probability table and a counting argument.
6:50ENThe Perils of Dogsitting: A Probability Warm-UpSawyer · Jane StreetSawyer introduces a five-night dogsitting puzzle and reviews independence, overlapping events and complements with coins and dice.
7:15ENA Balanced Game of War and the Probability of Three TaxisSawyer · Jane StreetSawyer introduces conditional probability through a card-game challenge, then solves an earlier six-car puzzle in two ways.