Probability - November 2005, All Stages

Problems

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Three Ball Line Up

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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Domino Pick

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

Are these domino games fair? Can you explain why or why not?

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Two and One

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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Odds or Sixes?

Stage: 2 Challenge Level: Challenge Level:1

Use the interactivity or play this dice game yourself. How could you make it fair?

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The Twelve Pointed Star Game

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

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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Flippin' Discs

Stage: 3 Challenge Level: Challenge Level:1

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

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Cosy Corner

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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Two's Company

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

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

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Odds and Evens

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

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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The Better Bet

Stage: 4 Challenge Level: Challenge Level:1

So which is the better bet? Both games cost £1 to play. Getting two heads and two tails for £3 or £2 for every six when three dice are rolled.

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The Birthday Bet

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The next ten people coming into a store will be asked their birthday. If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?

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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?

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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Spinners

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

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

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Spread

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

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?