Activity 2 – Monte Carlo Simulation

Experiment: Rolling a Fair Die

In this experiment, we consider rolling a fair six-sided die.

Each die has six possible outcomes:
1, 2, 3, 4, 5, and 6.

Event: Getting a 6

The event we are interested in is getting a 6 when the die is rolled.

Since the die is fair:

• Total possible outcomes = 6

• Favourable outcomes = 1 (only the outcome 6)

Therefore, the theoretical probability is:

P(Getting a 6) = 1/6 = 0.1667 

Monte Carlo Simulation

To verify this probability, a Monte Carlo simulation was performed using Python in Google Colab.

The experiment was repeated 100,000 times using a random number generator to simulate rolling the die.

The simulated probability obtained was:

0.16615

Analysis

The simulated probability (0.16615) is very close to the theoretical probability (0.1667).

Since both values are nearly equal, the Monte Carlo simulation verifies the theoretical probability of getting a 6 when rolling a fair die.