Probability - Advanced

Why Do People Find Probability Unintuitive and Difficult?

Stage: 2, 3, 4 and 5

Uncertain about the likelihood of unexpected events? You are not alone!

The Derren Brown Coin Flipping Scam

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.

Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

Can you devise a fair scoring system when dice land edge-up or corner-up?

Knock-out

Stage: 5 Challenge Level: Challenge Level:1

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

Snooker

Stage: 5 Challenge Level: Challenge Level:1

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Weekly Challenge 37: Magic Bag

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A weekly challenge concerning combinatorical probability.

Snooker Frames

Stage: 5 Challenge Level: Challenge Level:1

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

Teams

Stage: 5 Challenge Level: Challenge Level:1

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

Bet You a Million

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Heads or Tails - the prize doubles until you win it. How much would you pay to play?

Voting Paradox

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

FA Cup

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

Spinners

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

How do scores on dice and factors of polynomials relate to each other?

Taking Chances Extended

Stage: 4 and 5

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

Succession in Randomia

Stage: 5 Challenge Level: Challenge Level:1

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Is Your DNA Unique?

Stage: 5 Challenge Level: Challenge Level:1

Use combinatoric probabilities to work out the probability that you are genetically unique!

Ante Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Use cunning to work out a strategy to win this game.