How likely? - November 2010, All Stages

In this month's problems we invite you to experiment with a range of situations whose outcomes may surprise you. Can you use mathematics to explain why you shouldn't be so surprised?

Problems

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Probable Words

Stage: 1 Challenge Level: Challenge Level:1

If you asked your mum/dad/friend to take you to the park today, what sort of response might you get?

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The Hair Colour Game

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

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In the Playground

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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The Car That Passes

Stage: 2 Challenge Level: Challenge Level:1

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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Probably ...

Stage: 2 Challenge Level: Challenge Level:1

You'll need to work in a group for this problem. The idea is to decide, as a group, whether you agree or disagree with each statement.

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Winning the Lottery

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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Sociable Cards

Stage: 3 Challenge Level: Challenge Level:1

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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What Does Random Look Like?

Stage: 3 Challenge Level: Challenge Level:1

Engage in a little mathematical detective work to see if you can spot the fakes.

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At Least One...

Stage: 3 and 4 Challenge Level: Challenge Level:1

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

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Mathsland National Lottery

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

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Do You Feel Lucky?

Stage: 3 and 4 Challenge Level: Challenge Level:1

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

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Last One Standing

Stage: 3 and 4 Challenge Level: Challenge Level:1

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

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Same Number!

Stage: 4 Challenge Level: Challenge Level:1

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

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Weekly Challenges

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

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

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Interactive Workout - Mathmo

Stage: 5 Short Challenge Level: Challenge Level:1

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

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Discussing Risk and Reward

Stage: 5 Challenge Level: Challenge Level:1

10 starting points for risk vs reward

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Dicey Dice

Stage: 5 Challenge Level: Challenge Level:1

Invent a set of three dice where each one is better than one of the others?

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X-dice

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

Explore these X-dice with numbers other than 1 to 6 on their faces. Which one is best?

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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.