Probability Problems

 PrisonersLet me tell you a story of a dangerous prison. There were N prisoners in that prison. It is guarante... Table TennisOne day you have invited Sohel bhai to come to East West University to see an intra-University table... Moderate 7/9/11 Divide Candy AgainThere are N boxes with candies numbered from 1 to N. The number of candies in the boxes numbered 1 t... Walking Down The RoadThere is an M meter long road with the leftmost point of the road being the 0 meter point and the ri... Moderate 32/45/154 ExplosionThere is a house named Larcana. It is a very weird house. There are exactly N rooms in total and bet... Moderate 30/35/94 Finding LinesAnnabel and Richard like to invent new games and play against each other. One day Annabel has a new ... Goku's TreeRecently Goku has discovered a rooted tree graph. Goku’s tree has N nodes, among them node 1 is the ... Expected ResultA witch has imprisoned Bob in the 1st room of the Central Witchland Hotel. The hotel is weird. All t... Building the NumberThis is a straight-froward problem. You will be given N. You have to find the expected value of buil... The Lucky DiceRay and Evangeline are playing a game named "The Lucky Dice". In this game, each player tosses up an... Moderate 38/58/190 Sheldon's Obtuse TriangleWe all know Sheldon Cooper from The Big Bang Theory. Recently he got his Nobel Prize. He likes polyg... Moderate 15/27/107 Expected OddnessAlita found a string of n characters where each character of the string is either '0' or '1'. The Od... Random GraphsThis problem is very easy. There's a graph of \$N\$ nodes. Each edge \$u-v\$ (\$u >= v ; u = v\$ is possib... Moderate 13/15/48 Earn Your CupcakeA delicious NxN grid is given to you. All the lattice points of this grid contain a cupcake each exc... Moderate 4/4/9 An Act of Uniformly Random KindnessAfter selling all the bitcoins that you bought back in 2010, you now find yourself with a huge amoun... Moderate 15/15/24 Morona Virus Arrived"Cover your nose and mouth with a bent elbow or tissue when you sneeze or cough." World has defeated... Game ShowAlex is participating in a game show. Mr. Phil is the host of the game. Alex is provided with an arr... Jimmy and JamyJimmy and Jamy are two brothers. They like to play with colored marble. Jimmy has N boxes with three... Moderate 9/10/19 The MatrixIn the metaphysical world of the Matrix, different people make their chessboards with their own spec... Moderate 58/61/88 Marbles Per SecondYou have a rooted tree of n nodes. If we traverse the tree from the root, let’s say the traversing o... PlantikIt is Argentina vs France in the football world cup final of 2022 in a parallel universe. You are a ... Moderate 1/2/2