4.2 Estimating Probabilities Using Simulation

Designing and Running a Simulation

A simulation uses chance to model a random situation. Here is the systematic process:

Step 1: State the question — What probability do we want to estimate? Step 2: Assign random digits — Map digits 0-9 to outcomes Step 3: Simulate one trial — Use random digits to represent one occurrence Step 4: Repeat many trials — 50-100+ is typical Step 5: Compute the estimate — Count favorable trials / total trials

Example: Three free throws, each made 70% of the time. Estimate ${P(\text{make all 3})}$:

True probability: ${0.7^3 = 0.343}$ — simulation should approach this with more trials.