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.
1. Determine the total number of possible combinations of house models and garage/carport options. In this case, there are 6 house models and 2 options for each model (garage or carport), so there are a total of 6*2 = 12 possible combinations.
2. Assign probabilities to each of the 12 combinations. For example, if each combination is equally likely, then each combination would have a probability of 1/12.
3. Use a random number generator to simulate a large number of clients making choices. For each client, randomly select one of the 12 combinations.
4. Keep track of the number of clients who choose model B with a car garage. This will give you the frequency of this specific combination occurring in your simulation.
5. Repeat the simulation multiple times to generate a distribution of frequencies. The proportion of clients choosing model B with a car garage in the simulated data can be used as an estimate of the probability of this outcome occurring in the real world.
Use the results of the simulation to calculate the probability that a client
will choose model B with a car garage
To calculate the probability that a client will choose model B with a car garage based on the results of the simulation, you can use the following formula:
Probability = Number of clients choosing model B with a car garage / Total number of clients
Here's an example of how you can calculate the probability based on the simulated data:
Let's say you ran the simulation 100 times and found that out of those 100 clients, 15 chose model B with a car garage.
Probability = 15 / 100
Probability = 0.15 or 15%
Therefore, based on the simulated data, the estimated probability that a client will choose model B with a car garage is 15%.