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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?


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?

Concrete Calculation

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?

Scratch Cards

Age 14 to 16
Challenge Level

Mail order companies often send a scratch card with their catalogue. These cards are used to encourage people to order from the catalogue by offering a free prize. You have to uncover three of the numbers by scratching off the cover and revealing the number under three of the circles. Of course the numbers under the circles are randomly placed. If the numbers add up to more than fifteen you win a prize. What is the probability of winning a prize?