A large company plans to develop a private subdivision. There are 6 house models to choose from (models A, B, C, D, E, and F) and for each model, a client may opt to have a garage or a carport.

Part 1: What is the probability of a client who will choose model B with a garage?

(2 points)
Responses

36
3 sixths

26
2 sixths

212
2 over 12

112
1 over 12
Question 2
Part 2: Which chart correctly displays all the possible choices a client has when selecting a new home from this builder?(2 points)
Responses

Possible Choices
Model A + garage

Model B + garage

Model C + garage

Model D + garage

Model E + garage

Model F + garage



Possible Choices Model A + garage Model B + garage Model C + garage Model D + garage Model E + garage Model F + garage

Possible Choices
Model A + carport

Model B + carport

Model C + carport

Model D + garage

Model E + garage

Model F + garage

Possible Choices Model A + carport Model B + carport Model C + carport Model D + garage Model E + garage Model F + garage

Possible Choices
Model A + garage Model A + carport

Model B + garage Model B + carport

Model C + garage Model C + carport

Model D + garage Model D + carport

Model E + garage Model E + carport

Model F + garage Model F + carport

Possible Choices Model A + garage Model A + carport Model B + garage Model B + carport Model C + garage Model C + carport Model D + garage Model D + carport Model E + garage Model E + carport Model F + garage Model F + carport

Possible Choices
Model A + garage Model A + carport

Model B + garage Model B + carport

Model C + garage Model C + carport

Model D + garage

Model E + garage

Model F + garage

1 answer

To answer your questions, let's break down each part.

Part 1: Probability of Choosing Model B with a Garage

There are 6 house models (A, B, C, D, E, and F) and for each model, a client can choose between a garage or a carport.

Thus, the total options available for a client are:

  • Model A + Garage
  • Model A + Carport
  • Model B + Garage
  • Model B + Carport
  • Model C + Garage
  • Model C + Carport
  • Model D + Garage
  • Model D + Carport
  • Model E + Garage
  • Model E + Carport
  • Model F + Garage
  • Model F + Carport

So, there are a total of \(6 \text{ models} \times 2 \text{ options} = 12 \text{ total choices}\).

The specific choice of Model B with a garage is just 1 of these options.

Therefore, the probability of a client choosing Model B with a garage is:

\[ P(\text{Model B with Garage}) = \frac{1}{12} \]

From the responses you provided, the correct answer is:

112 (1 over 12)


Part 2: Correct Chart for Possible Choices

To summarize, a client has the following combinations to choose from:

  • Model A + Garage
  • Model A + Carport
  • Model B + Garage
  • Model B + Carport
  • Model C + Garage
  • Model C + Carport
  • Model D + Garage
  • Model D + Carport
  • Model E + Garage
  • Model E + Carport
  • Model F + Garage
  • Model F + Carport

The chart that correctly displays all the possible choices for a client when selecting a new home must include each house model combined with both options (Garage and Carport).

From the answers provided, the correct chart is:

Possible Choices
Model A + garage Model A + carport
Model B + garage Model B + carport
Model C + garage Model C + carport
Model D + garage Model D + carport
Model E + garage Model E + carport
Model F + garage Model F + carport

This chart lists all the combinations, satisfying the requirement for displaying all possible choices.