Question

Is the spinner shown a fair spinner? If yes, explain why. If not, describe a change that could make the spinner fair.
Explain

Answer 1

I don’t see the spinner image you mention. Could you upload or describe it (how many colored sectors, their shapes/sizes)?

Meanwhile, here is how to decide and how to fix it:

How to tell if a spinner is fair
- A standard circular spinner is fair when each outcome (color/sector) has the same probability. For a spinner where the pointer lands uniformly at random by angle, that happens exactly when every sector subtends the same central angle at the center of the circle. Equivalently (if all sectors run from the center to the same outer radius) each sector has equal area.
- Practically: use a protractor to measure the central angle of each sector. If every sector’s angle = 360°/n (where n = number of outcomes), the spinner is fair.

How to make an unfair spinner fair
- If some sectors are larger (larger central angles) than others, redraw the dividing radii so each sector has central angle 360°/n. For example, for 5 outcomes each sector should be 72°.
- If the spinner has an inner hole or differing radii for some sectors, make sure every sector covers the same angular span; if areas are used to define outcomes (not angle), adjust so their areas are equal.

If you upload the picture I’ll check the angles and tell you specifically whether it’s fair and what change(s) to make.