Monte Carlo simulation basics in NumPy - Mini Project: Build & Apply

Monte Carlo Simulation Basics

📖 Scenario: Imagine you want to estimate the chance of rolling a total of 7 with two dice. Instead of calculating all possibilities, you can simulate rolling dice many times and see how often you get 7.

🎯 Goal: You will build a simple Monte Carlo simulation using numpy to estimate the probability of rolling a sum of 7 with two dice.

📋 What You'll Learn

Use numpy to generate random dice rolls

Simulate rolling two dice many times

Count how many times the sum is exactly 7

Calculate the estimated probability

Print the final probability

💡 Why This Matters

🌍 Real World

Monte Carlo simulations are used in finance, science, and engineering to estimate probabilities and risks when exact math is difficult.

💼 Career

Data scientists use Monte Carlo methods to model uncertainty and make predictions based on random sampling.

1

Create dice roll simulation data

Import numpy as np and create a variable called rolls that simulates rolling two dice 10000 times using np.random.randint(1, 7, size=(10000, 2)).

NumPy

# Import numpy and create the dice rolls array
# Your code here

Need a hint?

Use np.random.randint to generate random integers from 1 to 6 for two dice, 10000 times.

2

Set the target sum for the dice

Create a variable called target_sum and set it to 7 to represent the sum we want to check for.

NumPy

import numpy as np
rolls = np.random.randint(1, 7, size=(10000, 2))
# Set the target sum to 7
# Your code here

Need a hint?

Just assign the number 7 to a variable named target_sum.

3

Calculate how many rolls sum to the target

Create a variable called count_target that counts how many rows in rolls have a sum equal to target_sum. Use np.sum and boolean indexing with rolls.sum(axis=1) == target_sum.

NumPy

import numpy as np
rolls = np.random.randint(1, 7, size=(10000, 2))
target_sum = 7
# Count how many rolls sum to 7
# Your code here

Need a hint?

Use rolls.sum(axis=1) to get sums of each roll, then compare to target_sum, then sum the True values.

4

Calculate and print the estimated probability

Calculate the estimated probability by dividing count_target by the total number of rolls (10000). Store it in probability. Then print the probability with print(probability).

NumPy

import numpy as np
rolls = np.random.randint(1, 7, size=(10000, 2))
target_sum = 7
count_target = np.sum(rolls.sum(axis=1) == target_sum)
# Calculate and print the probability
# Your code here

Need a hint?

Divide count_target by 10000 and print the result. The output should be a decimal number close to 0.17.