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. a. 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.
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To design a simulation for this scenario, we can create a simple program to randomly select a house model and whether the client opts for a garage or carport. Here's a basic outline of the simulation:
1. Define the probabilities of choosing each house model (A, B, C, D, E, F) and whether the client will choose a garage or carport for each model. These probabilities can be based on market research or historical data.
2. Create a loop that runs the simulation a large number of times (e.g. 10,000) to generate frequencies for each possible outcome.
3. Within each iteration of the loop, randomly select a house model from the options (A, B, C, D, E, F) based on their respective probabilities.
4. If the house model selected is B, randomly determine whether the client chooses a garage or carport based on the probabilities for model B.
5. Keep track of the frequency of clients choosing model B with a car garage.
6. After running the simulation for a large number of iterations, calculate the approximate probability of a client choosing model B with a car garage by dividing the frequency of this outcome by the total number of iterations.
Here's a basic Python implementation of this simulation:
```python
import random
# Define probabilities for choosing each house model and garage/carport option
house_probabilities = {'A': 0.1, 'B': 0.2, 'C': 0.15, 'D': 0.15, 'E': 0.2, 'F': 0.2}
garage_probabilities = {'B': {'garage': 0.6, 'carport': 0.4}}
# Initialize frequencies
b_with_garage_count = 0
# Run simulation for 10,000 iterations
num_iterations = 10000
for _ in range(num_iterations):
# Randomly select a house model based on probabilities
house_model = random.choices(list(house_probabilities.keys()), weights=list(house_probabilities.values()))[0]
# For model B, randomly determine garage or carport based on probabilities
if house_model == 'B':
garage_type = random.choices(['garage', 'carport'], weights=list(garage_probabilities['B'].values()))[0]
if garage_type == 'garage':
b_with_garage_count += 1
# Calculate probability of choosing model B with a car garage
prob_b_with_garage = b_with_garage_count / num_iterations
print('Approximate probability of choosing model B with a car garage:', prob_b_with_garage)
```
This simulation will provide an approximation of the probability of a client choosing model B with a car garage based on the defined probabilities. You can adjust the probabilities and number of iterations to further refine the accuracy of the approximation.