Question

plications of probability and
a spinner is divided into eight equal - sized sections, numbered from 1 to 8, inclusive
what is true about spinning the spinner one time? choose three correct answers.
$s = \\{1, 2, 3, 4, 5, 6, 7, 8\\}$
if a is a subset of s, a could be $\\{1, 2, 3\\}$.
if a subset a represents the complement of spinning an odd number, then $a = \\{2, 4, 6, 8\\}$.
if a subset a represents spinning a number less than 4, then $a = \\{1, 2, 3, 4\\}$.
if a is a subset of s, a could be $\\{7, 8, 9\\}$.

Explanation:

1. First Statement (\( S = \{1, 2, 3, 4, 5, 6, 7, 8\} \)): The sample space \( S \) includes all possible outcomes (numbers 1–8), so this is correct.
2. Second Statement (If \( A \) is a subset of \( S \), \( A \) could be \( \{1, 2, 3\} \)): A subset contains elements only from \( S \). \( \{1, 2, 3\} \) uses elements from \( S \), so this is valid.
3. Third Statement (Complement of odd numbers): Odd numbers in \( S \) are \( \{1, 3, 5, 7\} \). The complement (even numbers) is \( \{2, 4, 6, 8\} \), so this is correct.
4. Fourth Statement (Numbers less than 4): Numbers less than 4 are \( \{1, 2, 3\} \) (since 4 is not less than 4). So \( A = \{1, 2, 3, 4\} \) is incorrect.
5. Fifth Statement (\( \{7, 8, 9\} \)): 9 is not in \( S \), so this is not a subset.

Answer:

The three correct answers are:

• \( S = \{1, 2, 3, 4, 5, 6, 7, 8\} \)
• If \( A \) is a subset of \( S \), \( A \) could be \( \{1, 2, 3\} \)
• If a subset \( A \) represents the complement of spinning an odd number, then \( A = \{2, 4, 6, 8\} \)