Design and interpret a probability simulation

A target experiment selects one item from a finite population. The category counts are circle: 2, square: 4, with total 6

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

The target probability is \(\Pr(E)\) = \(\frac{2}{3}\)

The simulation used the following procedure

Use a random-number generator that returns one of the integers 1 to 12 with equal probability

Map outcomes 1 to 4 to circle and outcomes 5 to 12 to square

Reset the device before the next trial

Treat one complete selection as one trial

Run 1 recorded circle: 5, square: 7, giving 12 trials in total