Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are circle: 4, square: 6, triangle: 5, with total 15

The selected item is not returned before the next trial. Let \(E\) be the event that the outcome is circle

The initial population proportion is \(\Pr(E)\) = \(\frac{4}{15}\)

Later probabilities depend on what has been removed. Use the initial population proportion only as the reference when comparing recorded relative frequencies

The simulation used the following procedure

Use a spinner divided into 15 equal sectors

Map outcomes 1 to 4 to circle, outcomes 5 to 10 to square and outcomes 11 to 15 to triangle

Exclude the selected numbered outcome from later selections in this run. If it appears again on a spinner or random-number device, redraw without counting a new trial. Restore every outcome before a new run

Treat one complete selection as one trial

Run 1 recorded circle: 3, square: 6, triangle: 5, giving 14 trials in total