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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 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.

make it like a 7th grader is doing this, nothing too complicated please.

1 answer

Sure! Let's make this fun and easy to understand. We'll walk through how to simulate the choices, count the results, and find out how likely it is that someone will choose model B with a garage.

Step 1: Understand the Choices

  1. House Models: There are 6 models labeled A, B, C, D, E, and F.
  2. Garage or Carport: For each house model, a client can choose either a garage or a carport.

This means that for each of the 6 models, there are 2 choices (garage or carport). So, we have the following combinations:

  • A with Garage
  • A with Carport
  • B with Garage
  • B with Carport
  • C with Garage
  • C with Carport
  • D with Garage
  • D with Carport
  • E with Garage
  • E with Carport
  • F with Garage
  • F with Carport

That gives us a total of 12 different options!

Step 2: Set Up a Simulation

To simulate this, we can use a simple program (or even do it by hand if you prefer). Let's say we are going to simulate 1000 clients choosing a model and a type of parking.

You can use a computer program or do it by random selection. Let’s say we have a dice-like system where:

  • Roll a "1" or "2" for Garage, and
  • Roll a "3" or "4" for Carport.
  • Use another die (or a random number generator) to select the house model (1 through 6).

Here’s a basic way to simulate this using a computer program like Python, but you can think of it in simple terms:

import random

# Counts for each choice
total_clients = 1000
model_B_garage_count = 0
total_choices = 0

for _ in range(total_clients):
    # Randomly choose a house model (1 to 6)
    model_choice = random.randint(1, 6)
    
    # Randomly choose Garage (1, 2) or Carport (3, 4)
    parking_choice = random.randint(1, 4)
    
    # Check if the choice is Model B with a Garage
    if model_choice == 2 and parking_choice <= 2:  # Model B is 2
        model_B_garage_count += 1

    total_choices += 1

# Calculate probability
probability_B_garage = model_B_garage_count / total_choices

# Print results
print("Number of clients who chose Model B with Garage:", model_B_garage_count)
print("Estimated probability of choosing Model B with Garage:", probability_B_garage)

Step 3: Analyze the Results

Run the simulation, and you’ll get a number for how many clients chose Model B with a garage.

Finally, divide the number of clients that chose Model B with a garage by the total number of clients (which is 1000 in this example) to find the probability.

Example of Possible Outputs:

  • “Number of clients who chose Model B with Garage: 85”
  • “Estimated probability of choosing Model B with Garage: 0.085” (which is 8.5%)

Step 4: Conclusion

Through this simulation, you can see how often clients would likely choose Model B with the garage among a large number of clients, which gives you an estimate of that probability. You can try running the simulation multiple times to see how the results might change!

And that’s it! You’ve successfully simulated and approximated the probability of a client choosing Model B with a garage. Great job!