Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are low: 5, middle: 19, high: 8, peak: 8, with total 40

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

The initial population proportion is \(\Pr(E)\) = \(\frac{2}{5}\)

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 container holding 40 equally likely numbered tokens

Map outcomes 1 to 5 to low, outcomes 6 to 24 to middle, outcomes 25 to 32 to high and outcomes 33 to 40 to peak

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 low: 0, middle: 6, high: 1, peak: 1, giving 8 trials in total