What a Simulation Is

A simulation models a real-world process using abstraction and code. It includes features relevant to the question being studied and omits irrelevant details. A coin-flip simulation models 50/50 probability. It omits coin physics, weight, air resistance. The abstraction is intentional.

import random

def simulate_flips(n):
    heads = 0
    for i in range(n):
        if random.randint(0,1)==0:
            heads = heads + 1
    return heads / n

print(simulate_flips(1000))

heads <- 0
REPEAT 1000 TIMES
{
    flip <- RANDOM(0,1)
    IF flip = 0
    { heads <- heads+1 }
}
DISPLAY(heads / 1000)

Benefits and Limitations

Benefits: safe (test dangerous scenarios), cheap, fast, repeatable.
Limitations: accuracy depends on the model's assumptions; random seed affects results; real systems have complexity models omit.

AP exam point: A simulation is NEVER the same as the real world. A simulation showing 52% heads does NOT prove the coin is biased.

Practice Problems