A large company plans to develop a private subdivision. There are 6 house

Question

models to choose from and for each model, a client may opt to have a garage
or a carport. Use A, B, C, D, E, and F as labels for the house models.

a. Design and run a simulation to generate frequencies that can be used to approximate the probability of a client who will choose model B with a car garage.

Answer 1

To design and run a simulation for generating frequencies that can approximate the probability of a client choosing model B with a garage in the context of the subdivision, we will follow these steps:

1. Define the Models and Options: We have 6 house models labeled A, B, C, D, E, and F. For each model, the client can choose between two options: a garage or a carport. This results in 12 possible combinations (6 house models x 2 options).

2. Simulation Parameters:

   • Assume that each house model and option is equally likely to be chosen.
   • We will simulate a certain number of clients selecting their preferences.

3. Run the Simulation: We will randomly generate the selections for a significant sample size.

4. Collect and Analyze Results: Count how many clients chose model B with a garage, and compute the frequency to approximate the probability.

Python Code Simulation

import random

# Define house models and options
house_models = ['A', 'B', 'C', 'D', 'E', 'F']
options = ['Garage', 'Carport']

# Simulation parameters
num_clients = 10000  # total number of clients to simulate
model_B_garage_count = 0  # count for model B with garage

# Run simulation
for _ in range(num_clients):
    model_choice = random.choice(house_models)  # randomly choose a house model
    option_choice = random.choice(options)  # randomly choose an option (garage or carport)
    
    if model_choice == 'B' and option_choice == 'Garage':
        model_B_garage_count += 1  # count the choice for model B with garage

# Calculate frequencies and approximate probability
probability_model_B_garage = model_B_garage_count / num_clients

# Print results
print(f"Number of clients choosing model B with a garage: {model_B_garage_count}")
print(f"Approximate probability of choosing model B with a garage: {probability_model_B_garage:.4f}")

Explanation of the Code

1. We import the random library to help with random selections.
2. We create lists to store the house models and options (garage and carport).
3. We set the number of clients to simulate.
4. We loop through the number of clients:
   • For each client, we randomly choose a house model and an option.
   • We count how many times model B with a garage is chosen.
5. Finally, we calculate the approximate probability and print the results.

Running the Simulation

You can run this code in a Python environment. Adjust num_clients to a higher or lower value as needed to get more accurate approximations—more clients generally lead to better frequency approximations.

The output will provide you with the number of clients who chose model B with a garage and the estimated probability based on your simulation.