# Probability Problems

 PrisonersLet me tell you a story of a dangerous prison. There were N prisoners in that prison. It is guarante... Very Easy 170/179/249 ExplosionThere is a house named Larcana. It is a very weird house. There are exactly N rooms in total and bet... Moderate 18/22/62 Marbles Per SecondYou have a rooted tree of nnn nodes. If we traverse the tree from the root, let’s say the traversing... Moderate 1/1/1 Table TennisOne day you have invited Sohel bhai to come to East West University to see an intra-University table... Moderate 6/8/10 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 30/43/151 Finding LinesAnnabel and Richard like to invent new games and play against each other. One day Annabel has a new ... Moderate 5/6/25 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 to... Moderate 34/54/178 Sheldon's Obtuse TriangleWe all know Sheldon Cooper from The Big Bang Theory. Recently he got his Nobel Prize. He likes polyg... Moderate 13/24/92 Expected OddnessAlita found a string of n characters where each character of the string is either '0' or '1'. The Od... Moderate 8/10/21 Random GraphsThis problem is very easy. There's a graph of NNN nodes. Each edge u−vu-vu−v (u>=v;u=vu >= v ;... Moderate 11/13/46 Earn Your CupcakeA delicious NxN grid is given to you. All the lattice points of this grid contain a cupcake each exc... Moderate 2/2/4 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 13/13/22 Morona Virus Arrived"Cover your nose and mouth with a bent elbow or tissue when you sneeze or cough." World ha... 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 NNN boxes with thr... Moderate 5/6/11 The MatrixIn the metaphysical world of the Matrix, different people make their chessboards with their own spec... Moderate 48/51/74