Question

eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. subset a of the sample space represents the complement of the event in which the number 6 is drawn from the bag. which shows subset a? a = {6} a = {1, 2, 3, 4, 5, 6, 7, 8} a = {1, 3, 5, 7} a = {1, 2, 3, 4, 5, 7, 8}

Explanation:

Step1: Define the sample space

The sample space \( S \) is the set of all possible outcomes. Here, the numbers on the slips are from 1 to 8, so \( S=\{1, 2, 3, 4, 5, 6, 7, 8\} \).

Step2: Define the event and its complement

Let \( E \) be the event of drawing the number 6. Then \( E = \{6\} \). The complement of an event \( E \), denoted \( E^c \) (or subset \( A \) here), is the set of all outcomes in the sample space that are not in \( E \). So we need to remove 6 from the sample space.

Step3: Find subset \( A \)

Removing 6 from \( S=\{1, 2, 3, 4, 5, 6, 7, 8\} \) gives \( A=\{1, 2, 3, 4, 5, 7, 8\} \).

Answer:

\( A = \{1, 2, 3, 4, 5, 7, 8\} \) (the last option among the given choices)