To create a sample space for two-digit numbers using the digits 6, 8, 3, and 5, we will use the digits for the tens place (columns) and the ones place (rows).
Here's how we set up the table:
\[ \begin{array}{c|c|c|c|c} & 6 & 8 & 3 & 5 \ \hline 6 & 66 & 68 & 63 & 65 \ \hline 8 & 86 & 88 & 83 & 85 \ \hline 3 & 36 & 38 & 33 & 35 \ \hline 5 & 56 & 58 & 53 & 55 \ \end{array} \]
Now, to fill in the table:
- The entry at row \(6\), column \(6\) is \(66\).
- The entry at row \(6\), column \(8\) is \(68\).
- The entry at row \(6\), column \(3\) is \(63\).
- The entry at row \(6\), column \(5\) is \(65\).
Continuing this process for other rows:
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The entry at row \(8\), column \(6\) is \(86\).
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The entry at row \(8\), column \(8\) is \(88\).
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The entry at row \(8\), column \(3\) is \(83\).
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The entry at row \(8\), column \(5\) is \(85\).
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The entry at row \(3\), column \(6\) is \(36\).
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The entry at row \(3\), column \(8\) is \(38\).
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The entry at row \(3\), column \(3\) is \(33\).
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The entry at row \(3\), column \(5\) is \(35\).
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The entry at row \(5\), column \(6\) is \(56\).
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The entry at row \(5\), column \(8\) is \(58\).
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The entry at row \(5\), column \(3\) is \(53\).
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The entry at row \(5\), column \(5\) is \(55\).
Now, your complete sample space is:
\[ \begin{array}{c|c|c|c|c} & 6 & 8 & 3 & 5 \ \hline 6 & 66 & 68 & 63 & 65 \ \hline 8 & 86 & 88 & 83 & 85 \ \hline 3 & 36 & 38 & 33 & 35 \ \hline 5 & 56 & 58 & 53 & 55 \ \end{array} \]