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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?
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?
Escalator
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?
Age 14 to 16 Challenge Level:
You might like to imagine cutting the mound of earth into a cuboid, four prisms and four little pyramids in the corners. You'll need the formula (Area of base x Height)/3 for the volume of a pyramid.
NRICH is part of the family of activities in the Millennium Mathematics Project.