Question

1. joy can choose to ride the bus, walk, or carpool to school on thursday and friday. create a tree diagram to display the sample space.

Explanation:

Step1: Define first day choices

List Thursday's 3 options: Bus (B), Walk (W), Carpool (C) as first-level branches.

Step2: Add second day branches

For each Thursday choice, add 3 Friday branches (B, W, C).

Step3: List sample space outcomes

Combine each path to get all 9 possible outcomes.

Answer:

Tree Diagram Structure:

Start
├─ Thursday: Bus
│  ├─ Friday: Bus → (Bus, Bus)
│  ├─ Friday: Walk → (Bus, Walk)
│  └─ Friday: Carpool → (Bus, Carpool)
├─ Thursday: Walk
│  ├─ Friday: Bus → (Walk, Bus)
│  ├─ Friday: Walk → (Walk, Walk)
│  └─ Friday: Carpool → (Walk, Carpool)
└─ Thursday: Carpool
   ├─ Friday: Bus → (Carpool, Bus)
   ├─ Friday: Walk → (Carpool, Walk)
   └─ Friday: Carpool → (Carpool, Carpool)

Sample Space:

$\{(Bus, Bus), (Bus, Walk), (Bus, Carpool), (Walk, Bus), (Walk, Walk), (Walk, Carpool), (Carpool, Bus), (Carpool, Walk), (Carpool, Carpool)\}$