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Fixing the Odds

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

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Scratch Cards

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

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At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

Where to Land

Age 14 to 16 Challenge Level:

This printable worksheet may be useful: Where to Land.

Some useful questions:
How long will it take if Chris swims straight to the river bank?
Is the shortest distance the fastest?
What happens if Chris aims for land half way between the previous two points?