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
To design a simulation to generate frequencies for the probability of a client choosing model B with a car garage, we can follow these steps:
1. Define the probability of each house model being chosen:
- Model A: 0.15
- Model B: 0.25
- Model C: 0.10
- Model D: 0.20
- Model E: 0.15
- Model F: 0.15
2. Define the probability of a client opting for a garage:
- Garage: 0.60
- Carport: 0.40
3. Run a simulation to generate a large number of random selections of house models and garage/carport options.
4. For each selection, record whether the client chose model B with a car garage.
5. Calculate the frequency of clients choosing model B with a car garage over the total number of simulations to approximate the probability.
Here is a simple Python code snippet to simulate this scenario:
```python
import random
# Define probabilities
house_models = ['A', 'B', 'C', 'D', 'E', 'F']
model_probabilities = [0.15, 0.25, 0.10, 0.20, 0.15, 0.15]
garage_options = ['garage', 'carport']
garage_probabilities = [0.60, 0.40]
# Simulation parameters
num_simulations = 10000
num_b_with_garage = 0
# Run simulations
for _ in range(num_simulations):
chosen_model = random.choices(house_models, weights=model_probabilities)[0]
chosen_garage = random.choices(garage_options, weights=garage_probabilities)[0]
if chosen_model == 'B' and chosen_garage == 'garage':
num_b_with_garage += 1
# Calculate probability
probability_b_with_garage = num_b_with_garage / num_simulations
print('Probability of choosing model B with a car garage:', probability_b_with_garage)
```
This code will run the simulation to generate frequencies and approximate the probability of a client choosing model B with a car garage. The more simulations you run, the more accurate the probability estimate will be.