Question

each spinner is spun once to make a 2-digit number. a spin of 3 and 2 would be 32
complete the tree diagram to list all possible outcomes for spinning each spinner once.

Explanation:

Step1: Analyze the first spinner's first branch (1)

The first spinner's first outcome is 1. The second spinner has outcomes 1, 2, 3. So for the first branch (1 from first spinner), the middle node (second spinner's outcome) should be 2 (since 1, 2, 3 are the options and 1 and 3 are already there). So the middle square under 1 (first spinner) is 2. The two-digit number here would be 12 (but we just need the second spinner's outcome for the node, which is 2.

Step2: Analyze the middle tree (first spinner's middle outcome)

The first spinner's middle outcome: looking at the spinners, the first spinner has 1, 2, 3. The first tree is for 1, the middle tree is for 2 (since the first tree is 1, third is 3, so middle is 2). So the top square of the middle tree is 2. Then the left node (second spinner's outcome) should be 1 (since the second spinner has 1, 2, 3 and middle is 2, right is 3? Wait, no: the second spinner's outcomes are 1, 2, 3. So for the middle tree (first spinner is 2), the left node is 1, middle is 2, right is 3. Wait, the left square under the middle tree (top 2) should be 1, middle is 2, right is 3. Wait, the left node of the middle tree: the second spinner's first outcome is 1, so left square is 1. The right square is 3.

Step3: Analyze the third tree (first spinner's 3)

The first spinner's third outcome is 3. The second spinner's outcomes are 1, 2, 3. So the left node is 1, middle is 2, right is 3. So the left square under 3 (first spinner) is 1, middle is 2, right is 3 (but right is already 3, so middle is 2, left is 1).

Let's fill each square:

1. First tree (top 1): middle square (second spinner) is 2 (since outcomes are 1, 2, 3; 1 and 3 are present, so 2).
2. Middle tree (top square): first spinner's middle outcome is 2 (since first is 1, third is 3, so middle is 2). Then left square (second spinner) is 1, right square is 3.
3. Third tree (top 3): left square (second spinner) is 1, middle square is 2.

So:

• First tree (1): middle square: 2
• Middle tree (top): 2; left square: 1; right square: 3
• Third tree (3): left square: 1; middle square: 2

Let's list the squares:

First tree (1): middle square (between 1 and 3) → 2

Middle tree (top square) → 2; left square (left of 2) → 1; right square (right of 2) → 3

Third tree (3): left square (left of middle) → 1; middle square (middle) → 2

So the filled squares (from left to right, top to bottom of the tree diagram):

First tree middle: 2

Middle tree top: 2; middle tree left: 1; middle tree right: 3

Third tree left: 1; third tree middle: 2

Answer:

First tree middle square: 2
Middle tree top square: 2, middle tree left square: 1, middle tree right square: 3
Third tree left square: 1, third tree middle square: 2

(If we list the squares in the order of the diagram's empty boxes:
First empty (first tree middle): 2
Second empty (middle tree top): 2
Third empty (middle tree left): 1
Fourth empty (middle tree right): 3
Fifth empty (third tree left): 1
Sixth empty (third tree middle): 2)