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Welcome to NRICH.

Probability and combinatorics

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Simple probability

• 3 Motivate project: Taking chances
• 3 Probability of winning the U.K Lottery
• 3 Probability - Lotto
• 3 Probability of both mice in the same hat
• 3 Fairground spinner game
• 3 Rolling dice: how long until a double?
• 3 Lotteries: are consecutive numbers more likely?
• 4 Probability definitions
• 4 Probability of 3 birthdays on the same day
• 4 Probability that none of machine's components fail
• 4 Probability of Winning Tennis Match
• 4 Probability of success on Countdown
• 4 Population Percentages
• 4 Venn diagrams: probability of black shoes and no anorak
• 5 "Probability of A given B" question
• 5 Multiplying and adding probabilities
• 5 P(A|B)=P(AnB)/P(B) question
• 5 Casino odds on dice game
• 5 Probability of players meeting in a tournament
• 5 Danger in skydiving
• 5 Probability in Dice Rolling
• 5 Information content in dice rolling
• 5 Expected value in tossing coins
• 5 Chess expectation
• 5 Tennis tournament - players meeting
• 5 Buffon's needle problem
• 6 Probability of randomly choosing a mulitiple of 4 from the Natural Numbers
• 6 Dice rolling game
• 6 Gambling game
• 4 Gambling odds
• 6 Equal probability sphere

Conditional probability

• 3 Conditional probability
• 5 Conditional Probability- balls and bags
• 5 Probability of faults with three suppliers
• 5 Probability of defect with three suppliers
• 5 Bayes' Theorem
• 5 The Monty Hall problem

Probability models

• 5 Binomial probability question
• 5 When to use binomial, normal and geometric distributions
• 5 Formula for Probability distribution
• 5 Probability proofs using postulates
• 6 Probability density functions
• 6 Operations on probability distributions
• 5 Problems involving random variables and variance, expectation, etc

Combinatorics

Combinatorics is the area of maths concerned with finding out how many possibilities there are, or how many ways of doing something. Lots of investigations involve combinatorics.

• 3 Euler Problem
• 3 Sum of numbers made from 1,2,3,4,5
• 3 Article: Ding Dong Bell
• 3 1, 2 and 3
• 3 Emma's Dilemma
• 3 Nets of a cube
• 3 Pentominos
• 3 Pentominoes
• 3 Permutations puzzle
• 3 Spreading secrets problem
• 4 What's a permutation?
• 4 Choosing four different letters from L O N D O N
• 4 A Combinatorial Problem (covering a grid with tiles)
• 4 How many ways to make a cube from small cubes?
• 4 Colouring an octahedron
• 4 Counting problem
• 5 Dwarf height problem
• 4 Sum of three adjacent numbers on a wheel
• 4 Busy bee: bee moving on a hexagonal lattice
• 4 People at a party knowing each other (or not)
• 4 Missing numbers on two spun discs
• 5 Subsets of a 7-element Set
• 5 Permutations with repetition
• 5 Comb & Perm for seating arrangements
• 5 Arranging
• 5 Shuffling the deck problem
• 5 The counterfeit coin problem
• 5 The Josephus Problem
• 5 ₆C_x=15
• 5 Summing nCr
• 4 Tiling a grid with tetrominos
• 5 Hand shaking problem
• 5 Combinatorial problem
• 5 Combinatorics of polygon diagonals
• 5 Playing Cards
• 5 A Random Walk
• 5 Walks,Trails and Paths
• 5 Pigeon-hole problem
• 5 Pigeonhole principle problem
• 6 Relation in a power set

Graph theory

• 3 Spreading secrets problem
• 3 Hand-shaking problem
• 4 People at a party knowing each other (or not)
• 4 Article: Euler's Formula and Topology
• 4 The four colour map
• 4 Colouring an octahedron
• 5 Decision Maths - Simple Graph
• 5 Graph theory - possible graphs
• 5 Is this graph Hamiltonian?
• 5 The matching augmentation algorithm
• 6 Edges of bipartite subgraphs
• 6 Ramsey theory

Miscellaneous

• 3 Article: Transitivity
• 4 Benford's Law
• 4 Distribution of Easters
• 5 Probability of consecutives in lottery
• 5 Tying spaghetti ends: expected number of rings
• 5 Splitting bugs over the generations
• 5 Game show dilemma and a lot more besides
• 6 Sequences of Consecutive Integers: random walks and Markov chains