The rectangle shape in a set of blocks comes in two sizes( small and large ),three colors ( yellow, red, and blue ), and two thicknesses ( thick and thin )
A. Draw a tree diagram to find the total number of outcomes.
B. How many outcomes are possible?
A. To draw a tree diagram to find the total number of outcomes, we can start by identifying the choices for each of the three characteristics: size, color, and thickness.
1. Size: There are two options - small and large.
2. Color: There are three options - yellow, red, and blue.
3. Thickness: There are two options - thick and thin.
Start by drawing a root node representing the overall outcome. From the root node, draw three branches representing the three characteristics - size, color, and thickness. From each of these branches, draw additional branches representing the available options:
```
Size
/ \
Small Large
/ \ / \
Color Thickness Color Thickness
\ / \ / \
Yellow Thick Thin Red Thick Thin
| | | | |
Blue Thick Thin Blue Thick Thin
```
B. To determine the total number of outcomes, count the number of endpoints in the tree diagram. In this case, there are 2 endpoints for the size branch (Small and Large), 2 endpoints for the color branch (Yellow and Red), and 2 endpoints for the thickness branch (Thick and Thin).
To find the total number of outcomes, multiply the number of endpoints at each level:
2 (size) * 2 (color) * 2 (thickness) = 8
Therefore, there are 8 possible outcomes.