What it shows
A spinner with four equal sectors lands on each colour about a quarter of the time. A spinner with sectors of 180, 90, 45 and 45 degrees lands on the big colour about half the time and on each small colour about one eighth, showing that probability is the share of the circle.
The science
For a spinner the probability of a colour is the angle of its sector divided by 360 degrees. Equal sectors of 90 degrees each give probability one quarter. The unfair spinner gives one half, one quarter, one eighth and one eighth, which add to one. In a short run the observed fractions wobble, but as the number of spins grows they settle close to the predicted probability. This is the law of large numbers, and the gap between 40 spins and 200 spins makes it visible.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Two card circles of radius 8 cm
- A protractor and colours
- Two split pins and two card arrows, or a pencil and a paper clip
- A tally sheet
- A calculator
Safety
For this project: An adult must push the split pins through the card.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
Step by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Divide the first circle into four 90 degree sectors and colour them red, blue, green and yellow.
Divide the second circle into sectors of 180, 90, 45 and 45 degrees in the same four colours, with red for the 180 degree sector.
Fix an arrow at the centre of each with a split pin so it spins freely, or rest a pencil point at the centre and flick a paper clip.
Before spinning, write the predicted probability of each colour as a fraction and as a percentage.
Spin the fair spinner 40 times and tally, then compute each colour's share. Spin 200 times in total and recompute.
Do the same for the unfair spinner, keeping the arrow pivot clean so it does not stick on one side.
Draw bar charts of predicted and observed shares side by side for 40 and 200 spins.
Write a short conclusion on how the gap between prediction and observation changed with more spins.
What you should see
After 200 spins the fair spinner gives each colour close to 25 percent and the unfair one about 50, 25, 12.5 and 12.5 percent, with the 40-spin results further from prediction than the 200-spin ones.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01What is the probability of green on the unfair spinner if its sector is 45 degrees?
45 divided by 360, which is one eighth or 12.5 percent.
02Why do the probabilities of all colours add to 1?
The sectors together make the whole circle of 360 degrees, and the arrow must land somewhere.
03If you spin the fair spinner 4 times, must you get each colour once?
No. Probability describes the long run, not any single short set of spins.
04What is the law of large numbers in this experiment?
With more spins the observed share of each colour gets closer to its predicted probability.
Take it further
Spin both spinners together and record pairs to find how often both show red; compare with one quarter times one half.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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