Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are first: 29, second: 11, with total 40

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

The initial population proportion is \(\Pr(E)\) = \(\frac{11}{40}\)

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 random-number generator that returns one of the integers 1 to 40 with equal probability

Map outcomes 1 to 29 to first and outcomes 30 to 40 to second

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 first: 13, second: 3, giving 16 trials in total