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.

Question

For the simulation, I will use 2 die with 6 faces. The number that the first die lands on will be the house model.

(example: if I roll a 1, the house chosen is A)

The second die will choose if the house has a garage or carport. Rolling an even number means a garage. Rolling an odd number means a carport.

(Example: rolling a 2, 4, or 6 means its a garage.)

I will be conducting 15 trials.

Here are the results of the simulation.

B : Gar

C: Car

D: Car

D: Gar

F: Gar

D: Gar

A: Car

B: Gar

F: Gar

C: Gar

A: Gar

A: Gar

A: Gar

E: Gar

A: Gar

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

Answer 1

To calculate the probability that a client will choose model B with a garage, we need to analyze the results of your simulation.

From your simulation results, we have the following outcomes:

1. B: Gar
2. C: Car
3. D: Car
4. D: Gar
5. F: Gar
6. D: Gar
7. A: Car
8. B: Gar
9. F: Gar
10. C: Gar
11. A: Gar
12. A: Gar
13. A: Gar
14. E: Gar
15. A: Gar

Now, let's break down the results:

• Total trials: 15
• Occurrences of model B with a garage: 2 times (from results 1 and 8)

Probability Calculation

The probability \( P \) of an event is defined as:

\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

For model B with a garage:

• Favorable outcomes (B: Gar): 2
• Total outcomes: 15

So the probability \( P(B \text{ with Garage}) \) can be calculated as follows:

\[ P(B \text{ with Garage}) = \frac{2}{15} \]

Final Probability

Thus, the probability that a client will choose model B with a garage is:

\[ P(B \text{ with Garage}) \approx 0.1333 \text{ or } 13.33% \]