Probability - Advanced

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Why do people find probability unintuitive and difficult?

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

problem

The Derren Brown coin flipping scam

Age

16 to 18

Challenge level

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

problem

Dicey decisions

Age

16 to 18

Challenge level

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

problem

Knock-out

Age

16 to 18

Challenge level

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?

problem

Snooker

Age

16 to 18

Challenge level

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

problem

Magic bag

Age

16 to 18

Challenge level

A weekly challenge concerning combinatorical probability.

problem

Snooker frames

Age

16 to 18

Challenge level

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?

problem

Teams

Age

16 to 18

Challenge level

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

problem

Bet you a million

Age

14 to 16

Challenge level

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

problem

Voting paradox

Age

14 to 18

Challenge level

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?

problem

Fa cup

Age

16 to 18

Challenge level

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!