To determine the sample space for choosing one card from the set of eight cards labeled with the characters A, D, D, I, T, I, O, N, we need to list out all the unique elements within the set of cards. The sample space consists of all possible distinct outcomes when selecting one card.
Here’s how we can identify the unique elements:
1. Start with the given set: A, D, D, I, T, I, O, N.
2. Identify and list each unique letter that appears in the set.
- The letter "A" appears once.
- The letter "D" appears twice.
- The letter "I" appears twice.
- The letter "T" appears once.
- The letter "O" appears once.
- The letter "N" appears once.
Since we are looking for a set of unique elements, we will not repeat any letters, even if they appear multiple times.
Now, let’s list the unique letters in the set:
A, D, I, T, O, N.
Therefore, the sample space, which includes all distinct elements from the given set of cards, is:
[tex]\[ S = \{A, D, I, T, O, N\} \][/tex]
Thus, the correct answer is:
[tex]\[ S = \{A, D, I, T, O, N\} \][/tex]
