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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?


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?

Tree Tops

Age 14 to 16
Challenge Level
One way to get started is to imagine what would happen if you planted 1 hectare with Sitka Spruce.
This would cost £120 000.

After 10 years, you would get £10 000 from the 10-year thinning:
-120 000 + 10 000 = -110 000 so you have a loss of £110 000 after 10 years.

After another 10 years, you get £40 000 from the 20-year thinning:
-110 000 + 40 000 = -70 000 so your loss after 20 years is £70 000.

You could then choose to chop down your forest and sell the wood after another 10 years. This would bring in £358 000.
-70 000 + 358 000 = 288 000. So after 30 years, you have a profit of £288 000.

However, you could choose instead to keep the trees and cut down the forest after 40 years. This would bring in £513 000.
-70 000 + 513 000 = 443 000. So after 40 years, your profit would be £443 000.

Perhaps you could set up a spreadsheet to calculate the costs and profits for each type of tree!

If you want to maximise profits after 100 years, you could investigate planting a forest for 50 years, and then cutting it down and planting another 50-year forest.
Or planting a 60-year forest and a 40-year forest.
Or two 30-year forests and a 40-year forest.