Probability - November 2005, Stage 4&5

Problems

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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%?