Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are low: 1, middle: 2, high: 2, peak: 1, with total 6

The selected item is returned before the next trial. Let \(E\) be the event that the outcome is middle or peak

The target probability is \(\Pr(E)\) = \(\frac{1}{2}\)

The simulation used the following procedure

Use a container holding 18 equally likely numbered tokens

Map outcomes 1 to 3 to low, outcomes 4 to 9 to middle, outcomes 10 to 15 to high and outcomes 16 to 18 to peak

Reset the device before the next trial

Treat one complete selection as one trial

Run 1 recorded low: 4, middle: 5, high: 3, peak: 3, giving 15 trials in total