CBuilderLab· about 40 min· in the browser

Lab: simulate dice and compare with the theory

Estimate a probability with simulation (Monte Carlo) and see that the frequency approaches the theory as the number of trials grows.

Teaches: Probability — the basics

Requires: Python — lists, loops and dictionariesStatistics — mean, median and spread

Theory

P(the sum of two dice = 7) = 6/36 ≈ 0.167. Simulate 20,000 rolls with a fixed random seed and count the share of sevens. Relative frequency → probability (the law of large numbers).

Sub-tasks

kasta_tva(rng) — roll two — Return the sum of two dice rolls using rng.randint(1, 6).
andel_sjuor(n, seed) — share of sevens — Simulate n rolls with random.Random(seed) and return the share that came out as 7.
teoretisk_sannolikhet(summa) — theoretical probability — Return the exact probability of a given sum 2–12.

The starter code

runs in your browser

import random


def kasta_tva(rng):
    # TODO: summan av två kast med rng.randint(1, 6)
    ...


def andel_sjuor(n, seed=0):
    # TODO: rng = random.Random(seed); räkna hur många av n kast som blir 7
    ...


def teoretisk_sannolikhet(summa):
    # TODO: antal gynnsamma par (a, b) med a + b == summa, delat med 36
    ...

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Expected results

andel_sjuor(20000, 1) within ±0.01 of 0.1667; teoretisk_sannolikhet(7) = 6/36; teoretisk_sannolikhet(2) = 1/36.

Common mistakes

randint(1, 6) includes 6 (unlike range).
A new random seed in every call makes the result irreproducible — create Random(seed) once.
Counts sums 1–12 instead of 2–12.