The rectangle shape in a set of blocks comes in two sizes(small and large), three colors (yellow, red, and blue), and have two thicknesses, (thick and thin).
1. Draw a tree diagram to find the total number of outcomes.
2. How many outcomes are possible?
3. How many outcomes will be red?
4. How many outcome will be blue and thin?
2*3*2 = 12
4 of them are red (thick, thin, small Lg)
2 of them (a small and a large)
-----------------red
---------small --yellow
-----------------blue
thick
------------------ red
---------large --- yellow
-------------------blue
-------------------red
---------small ----yellow
-------------------blue
thin
------------------ red
---------large ----yellow
-------------------blue
To answer these questions, we can use a tree diagram to visualize all the possible combinations.
1. Tree diagram:
SIZE
/ \
Small Large
/ \ / \
COLOR Yellow Red Blue Yellow Red Blue
/ \ / \ / \ /
THICK Thick Thin Thick Thin Thick Thin
In this tree diagram, we have three levels representing the three different attributes: size, color, and thickness.
2. To find the total number of outcomes, we need to multiply the number of possibilities at each level.
- For size, there are two options: small and large.
- For color, there are three options: yellow, red, and blue.
- For thickness, there are two options: thick and thin.
Using the multiplication principle, we calculate the total number of outcomes as:
2 (size options) x 3 (color options) x 2 (thickness options) = 12 outcomes.
So, there are 12 possible outcomes.
3. To find the number of outcomes that will be red, we look at the "red" branch in the tree diagram.
We can see that there are two possibilities: a small red rectangle and a large red rectangle.
Therefore, there are 2 outcomes that will be red.
4. To find the number of outcomes that will be blue and thin, we follow the "blue" branch in the tree diagram and consider only the "thin" branch.
We can see that there is one possibility: a small blue thin rectangle.
Therefore, there is 1 outcome that will be blue and thin.