Calculating Experimental Probabilities from Simulations

Property The experimental probability of an event based on a simulation is calculated using the formula: $$P(\text{event}) = \frac{\text{Number of successful trials}}{\text{Total number of trials}}$$.

Examples A simulation models a basketball player shooting free throws. Out of $50$ simulated trials, the player makes the shot $38$ times. The experimental probability of making a free throw is $P(\text{make}) = \frac{38}{50} = 0.76$, or $76\%$. A weather model simulates the chance of rain over $100$ days. The simulation results show rain on $22$ of those days. The experimental probability of rain is $P(\text{rain}) = \frac{22}{100} = 0.22$, or $22\%$. A factory uses a random number generator to simulate finding defective parts. In $200$ trials, $5$ defective parts are found. The experimental probability of a defective part is $P(\text{defective}) = \frac{5}{200} = 0.025$, or $2.5\%$.

Explanation After designing and running a simulation, you can use the gathered data to calculate the experimental probability of a real world event. This is done by dividing the number of times the desired outcome occurred by the total number of simulated trials. The more trials you run in your simulation, the closer your experimental probability will typically get to the actual theoretical probability. These simulated probabilities allow us to make predictions and informed decisions in real world scenarios where direct testing is too difficult, expensive, or time consuming.