Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are type A: 1, type B: 21, type C: 18, with total 40

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

The initial population proportion is \(\Pr(E)\) = \(\frac{39}{40}\)

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 outcome 1 to type A, outcomes 2 to 22 to type B and outcomes 23 to 40 to type C

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 type A: 0, type B: 13, type C: 7, giving 20 trials in total