Question

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

Design 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.
Use the results of the simulation to calculate the probability that a client will choose model B with a car garage.

Answer 1

To design a simulation to generate frequencies that can be used to approximate the probability of a client choosing model B with a car garage, we can follow these steps:

1. Create a list of options for each house model:
- Model A with car garage
- Model A with carport
- Model B with car garage
- Model B with carport
- Model C with car garage
- Model C with carport
- Model D with car garage
- Model D with carport
- Model E with car garage
- Model E with carport
- Model F with car garage
- Model F with carport

2. Set up a simulation that randomly selects a house model and garage/carport option for each client. Repeat this process for a large number of clients.

3. Count the frequency of clients who choose model B with a car garage.

4. Calculate the probability of a client choosing model B with a car garage by dividing the frequency of choosing that option by the total number of simulations.

Here is an example of a potential Python code for this simulation:

```python
import random

# Set up variables for simulation
total_simulations = 10000
model_b_car_garage_count = 0

# Simulate client choices
for _ in range(total_simulations):
choice = random.choice(['A_garage', 'A_carport',
'B_garage', 'B_carport',
'C_garage', 'C_carport',
'D_garage', 'D_carport',
'E_garage', 'E_carport',
'F_garage', 'F_carport'])

if choice == 'B_garage':
model_b_car_garage_count += 1

# Calculate probability
probability = model_b_car_garage_count / total_simulations
print("The probability of a client choosing model B with a car garage is:", probability)
```

By running this simulation with a large number of repetitions, we can approximate the probability of a client choosing model B with a car garage based on the frequencies generated.