Question

1. the sample space for game b is partially filled out. finish writing the outcomes in the sample space to show all possible outcomes. (___ / 2 points)

Explanation:

Step1: Analyze Cube 1 = 1 row

For Cube 1 = 1, Cube 2 = 5: \(1 + 5 = 6\); Cube 2 = 6: \(1 + 6 = 7\) (already filled, but pattern is sum of two cubes).

Step2: Analyze Cube 1 = 2 row

Cube 2 = 4: \(2 + 4 = 6\); Cube 2 = 5: \(2 + 5 = 7\); Cube 2 = 6: \(2 + 6 = 8\)

Step3: Analyze Cube 1 = 3 row

Cube 2 = 1: \(3 + 1 = 4\); Cube 2 = 2: \(3 + 2 = 5\); Cube 2 = 3: \(3 + 3 = 6\); Cube 2 = 4: \(3 + 4 = 7\) (already filled); Cube 2 = 5: \(3 + 5 = 8\); Cube 2 = 6: \(3 + 6 = 9\)

Step4: Analyze Cube 1 = 4 row

Cube 2 = 1: \(4 + 1 = 5\); Cube 2 = 2: \(4 + 2 = 6\); Cube 2 = 3: \(4 + 3 = 7\); Cube 2 = 4: \(4 + 4 = 8\); Cube 2 = 5: \(4 + 5 = 9\) (already filled); Cube 2 = 6: \(4 + 6 = 10\)

Step5: Analyze Cube 1 = 5 row

Cube 2 = 2: \(5 + 2 = 7\); Cube 2 = 3: \(5 + 3 = 8\); Cube 2 = 4: \(5 + 4 = 9\); Cube 2 = 5: \(5 + 5 = 10\); Cube 2 = 6: \(5 + 6 = 11\) (and Cube 2 = 1: \(5 + 1 = 6\) already filled)

Step6: Analyze Cube 1 = 6 row

Cube 2 = 1: \(6 + 1 = 7\); Cube 2 = 2: \(6 + 2 = 8\); Cube 2 = 3: \(6 + 3 = 9\); Cube 2 = 4: \(6 + 4 = 10\); Cube 2 = 5: \(6 + 5 = 11\); Cube 2 = 6: \(6 + 6 = 12\)

Now, filling each cell:

• Cube 1 = 1, Cube 2 = 5: \(1+5=6\) (filled as 6), Cube 2 = 6: \(1+6=7\) (filled)
• Cube 1 = 2:
• Cube 2 = 4: \(2+4=6\)
• Cube 2 = 5: \(2+5=7\)
• Cube 2 = 6: \(2+6=8\)
• Cube 1 = 3:
• Cube 2 = 1: \(3+1=4\)
• Cube 2 = 2: \(3+2=5\)
• Cube 2 = 3: \(3+3=6\)
• Cube 2 = 5: \(3+5=8\)
• Cube 2 = 6: \(3+6=9\)
• Cube 1 = 4:
• Cube 2 = 1: \(4+1=5\)
• Cube 2 = 2: \(4+2=6\)
• Cube 2 = 3: \(4+3=7\)
• Cube 2 = 4: \(4+4=8\)
• Cube 2 = 6: \(4+6=10\)
• Cube 1 = 5:
• Cube 2 = 2: \(5+2=7\)
• Cube 2 = 3: \(5+3=8\)
• Cube 2 = 4: \(5+4=9\)
• Cube 2 = 5: \(5+5=10\)
• Cube 2 = 6: \(5+6=11\)
• Cube 1 = 6:
• Cube 2 = 1: \(6+1=7\)
• Cube 2 = 2: \(6+2=8\)
• Cube 2 = 3: \(6+3=9\)
• Cube 2 = 4: \(6+4=10\)
• Cube 2 = 5: \(6+5=11\)
• Cube 2 = 6: \(6+6=12\)

Let's fill each cell systematically:

Cube 1 = 1 (already mostly filled, check 5 and 6: done)

Cube 1 = 2:

• (2,4): \(2+4=6\)
• (2,5): \(2+5=7\)
• (2,6): \(2+6=8\)

Cube 1 = 3:

• (3,1): \(3+1=4\)
• (3,2): \(3+2=5\)
• (3,3): \(3+3=6\)
• (3,5): \(3+5=8\)
• (3,6): \(3+6=9\)

Cube 1 = 4:

• (4,1): \(4+1=5\)
• (4,2): \(4+2=6\)
• (4,3): \(4+3=7\)
• (4,4): \(4+4=8\)
• (4,6): \(4+6=10\)

Cube 1 = 5:

• (5,2): \(5+2=7\)
• (5,3): \(5+3=8\)
• (5,4): \(5+4=9\)
• (5,5): \(5+5=10\)
• (5,6): \(5+6=11\)

Cube 1 = 6:

• (6,1): \(6+1=7\)
• (6,2): \(6+2=8\)
• (6,3): \(6+3=9\)
• (6,4): \(6+4=10\)
• (6,5): \(6+5=11\)
• (6,6): \(6+6=12\)

For example, the cell (Cube 1=4, Cube 2=4) is \(4 + 4 = 8\), (Cube 1=3, Cube 2=1) is \(3+1=4\), etc. The key is that each cell is the sum of the number on Cube 1 (row) and Cube 2 (column).

Answer:

To complete the sample space, each cell \((\text{Cube 1}, \text{Cube 2})\) is filled with \(\text{Cube 1} + \text{Cube 2}\). Here are the missing values:

• Cube 1 = 2 row:
• (2,4): \(2 + 4 = 6\)
• (2,5): \(2 + 5 = 7\)
• (2,6): \(2 + 6 = 8\)

• Cube 1 = 3 row:
• (3,1): \(3 + 1 = 4\)
• (3,2): \(3 + 2 = 5\)
• (3,3): \(3 + 3 = 6\)
• (3,5): \(3 + 5 = 8\)
• (3,6): \(3 + 6 = 9\)

• Cube 1 = 4 row:
• (4,1): \(4 + 1 = 5\)
• (4,2): \(4 + 2 = 6\)
• (4,3): \(4 + 3 = 7\)
• (4,4): \(4 + 4 = 8\)
• (4,6): \(4 + 6 = 10\)

• Cube 1 = 5 row:
• (5,2): \(5 + 2 = 7\)
• (5,3): \(5 + 3 = 8\)
• (5,4): \(5 + 4 = 9\)
• (5,5): \(5 + 5 = 10\)
• (5,6): \(5 + 6 = 11\)

• Cube 1 = 6 row:
• (6,1): \(6 + 1 = 7\)
• (6,2): \(6 + 2 = 8\)
• (6,3): \(6 + 3 = 9\)
• (6,4): \(6 + 4 = 10\)
• (6,5): \(6 + 5 = 11\)
• (6,6): \(6 + 6 = 12\)

(Note: The table is completed by summing the row (Cube 1) and column (Cube 2) values for each cell.)