Theoretical probability

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Favourite

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?
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Favourite

Limiting Probabilities

Age

16 to 18

Challenge level

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.
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Favourite

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!
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Favourite

In the Playground

Age

5 to 11

Challenge level

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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Favourite

The Car That Passes

Age

7 to 11

Challenge level

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
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Favourite

Roll These Dice

Age

7 to 11

Challenge level

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
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Favourite

Same or Different?

Age

7 to 11

Challenge level

Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.
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Favourite

The Twelve Pointed Star Game

Age

7 to 11

Challenge level

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
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Favourite

It's a Tie

Age

7 to 11

Challenge level

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
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Favourite

Flippin' Discs

Age

11 to 14

Challenge level

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?