Activity -2

In this activity, I conducted experiments to determine the probability of each number (1 to 6) appearing when rolling a fair six-sided die. I focused on three cases: rolling the die 10 times, 50 times, and 100 times.

First, I used Python to simulate die rolls and recorded how often each number occurred. I printed all outcomes to get a clearer picture of the results.

Next, I calculated the expected probabilities. For a fair die, each number (1–6) has an equal chance of appearing — approximately 16.67% (or 1/6).

To further validate the results, I used a Monte Carlo simulation. This involved running 1,000 experiments for each case (10, 50, and 100 rolls) and calculating the average probability of each number appearing.

Conclusion:

This experiment demonstrated how Monte Carlo simulations can be used to verify whether observed results align with theoretical probabilities. As the number of rolls increased, the observed frequencies of each number approached the expected 16.67%, showing the Law of Large Numbers in action.