To simulate an event with a $0.5$ probability, such as a fair coin toss, we can utilize a random number generator that outputs continuous values in the interval $[0, 1]$. By testing whether the generated float is greater than $0.5$, we assign the two outcomes with equal likelihood, since the probability of the value falling in either the $[0, 0.5]$ or $(0.5, 1]$ sub-interval is exactly $b-a = 0.5$.