Question

A spinner is divided into 4 equal sections labeled with the numbers 1 through 4. The tree
diagram represents all of the possible outcomes of spinning the spinner twice. Use the
drop-down menus to complete the statements about the possible outcomes.

1

2

3

4

1
2
3
4

1
2
3
4

1
2
3
4

1
2
3
4

Choose ...

Choose ...

possible outcomes for spinning two numbers that have a sum

possible outcomes.

Choose ...

possible outcomes for spinning the same number twice.

Click the arrows to choose an answer from each menu.

There are a total of

There are

greater than 5.

There are

Answer 1

Let's break down the questions regarding the outcomes of spinning a spinner divided into 4 equal sections labeled with the numbers 1 through 4.

1. **Total possible outcomes:**
When you spin the spinner twice, each spin has 4 possible outcomes. Thus, for two spins, the total number of outcomes is:
\[
4 \times 4 = 16
\]
So, **"There are a total of 16 possible outcomes."**

2. **Possible outcomes for spinning two numbers that have a sum greater than 5:**
The possible sums from two spins can range from 2 (1+1) to 8 (4+4). We need to identify the combinations where the sum is greater than 5. The combinations with sums greater than 5 are:
- (2, 4) → 2 + 4 = 6
- (3, 3) → 3 + 3 = 6
- (3, 4) → 3 + 4 = 7
- (4, 2) → 4 + 2 = 6
- (4, 3) → 4 + 3 = 7
- (4, 4) → 4 + 4 = 8
Counting these outcomes, we have the following pairs: (2, 4), (3, 3), (3, 4), (4, 2), (4, 3), and (4, 4), which gives us a total of **6 outcomes.**
Therefore, **"There are 6 possible outcomes for spinning two numbers that have a sum greater than 5."**

3. **Possible outcomes for spinning the same number twice:**
The outcomes where both spins result in the same number are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
This gives us 4 outcomes: (1, 1), (2, 2), (3, 3), (4, 4). Therefore, **"There are 4 possible outcomes for spinning the same number twice."**

Now you can fill in the statements accordingly:

- "There are a total of 16 possible outcomes."
- "There are 6 possible outcomes for spinning two numbers that have a sum greater than 5."
- "There are 4 possible outcomes for spinning the same number twice."