To determine the sample space for choosing one card from a set of seven cards labeled with the letters \( N, U, M, B, E, R, S \), we need to list all the possible outcomes.
The sample space is the set of all possible outcomes when one card is chosen. Each of the cards has a unique label, so each letter represents a distinct possible outcome.
Given the cards labeled with \( N, U, M, B, E, R, S \), the sample space consists of these letters. We list these letters in a set, which includes all possible outcomes of selecting one card from the set:
[tex]\[
S = \{ N, U, M, B, E, R, S \}
\][/tex]
We need to compare this set with the provided choices:
- \( S = \{ N, B, R, M, U \} \) - This set is incomplete as it is missing \( E \) and \( S \).
- \( S = \{ N, B, S, M, E, R, U \} \) - This set includes all the correct letters and matches our sample space.
- \( S = \{ B, U, S \} \) - This set is incomplete as it is missing \( N, M, E, R \).
- \( S = \{ M \} \) - This set is incomplete as it is missing \( N, U, B, E, R, S \).
Thus, the correct sample space for choosing one card is:
[tex]\[
S = \{ N, B, S, M, E, R, U \}
\][/tex]
So, the correct answer is:
[tex]\[
S = \{ N, B, S, M, E, R, U \}
\][/tex]
