When asked for the sample space for choosing one card from a set of seven cards labeled [tex]$N, U, M, B, E, R, S$[/tex], we need to identify all possible outcomes that can occur when one card is chosen from this set. The sample space should include every card that can be picked.
In this scenario, the set of labels is:
[tex]\[
\{N, U, M, B, E, R, S\}
\][/tex]
We need to identify which among the provided options correctly represents the full sample space:
1. [tex]\(S=\{N, B, R, M, U\}\)[/tex] – This set has only 5 elements and is missing some of the cards.
2. [tex]\(S=\{N, B, S, M, E, R, U\}\)[/tex] – This set contains all 7 elements: [tex]\(N\)[/tex], [tex]\(U\)[/tex], [tex]\(M\)[/tex], [tex]\(B\)[/tex], [tex]\(E\)[/tex], [tex]\(R\)[/tex], and [tex]\(S\)[/tex].
3. [tex]\(S=\{B, U, S\}\)[/tex] – This set has only 3 elements and is missing many of the cards.
4. [tex]\(S=\{M\}\)[/tex] – This set has only 1 element and is missing many of the cards.
The correct sample space, which includes all possible outcomes when choosing one card from the set, is:
[tex]\[
S = \{N, B, S, M, E, R, U\}
\][/tex]
Therefore, the correct answer is:
[tex]\[
S=\{N, B, S, M, E, R, U\}
\][/tex]
