Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are group A: 3, group B: 22, group C: 5, group D: 10, with total 40

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

The initial population proportion is \(\Pr(E)\) = \(\frac{1}{4}\)

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 40 equal sectors

Map outcomes 1 to 3 to group A, outcomes 4 to 25 to group B, outcomes 26 to 30 to group C and outcomes 31 to 40 to group D

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 group A: 1, group B: 11, group C: 2, group D: 6, giving 20 trials in total