AI Tutor
Imagine playing a game where spinning your favorite color wins you a prize! Would you rather your color have a tiny slice or a giant slice of the wheel?
A spinner is a flat circle divided into slices called sectors, with an arrow that spins freely around the center.
The theoretical probability of landing on a sector depends directly on its central angle ΞΈ\theta and size relative to the entire circle:
P(Event)=θ360∘=Sector AreaTotal AreaP(\text{Event}) = \frac{\theta}{360^\circ} = \frac{\text{Sector Area}}{\text{Total Area}}
What happens if we spin this arrow over and over again?
The theoretical probability P(Event)P(\text{Event}) of landing on a sector depends on its central angle θ\theta out of 360∘360^\circ: P(Event)=θ360∘=Sector AreaTotal AreaP(\text{Event}) = \frac{\theta}{360^\circ} = \frac{\textbf{Sector Area}}{\textbf{Total Area}}

Testing Our Spinner

From these trials, we calculate the Experimental Probability: ExperimentalΒ Probability=NumberΒ ofΒ TimesΒ OutcomeΒ OccursTotalΒ NumberΒ ofΒ SpinsΒ (Trials)\text{Experimental Probability} = \frac{\textbf{Number of Times Outcome Occurs}}{\textbf{Total Number of Spins (Trials)}}
When parts are not the same size, we call them unequal. The bigger a slice is, the more likely the arrow will stop there.
Each time we spin the arrow, we call it a trial, and we record the color it lands on with a tally mark.
From our tally counts, we can find the Experimental Probability of each color: