Answer :
To solve this problem, we will first understand the concept of the complement of an event in a sample space.
### Step-by-Step Solution
1. Identify the Sample Space:
The sample space in this context is the set of all possible outcomes when drawing a slip of paper from the bag. Since each slip contains a unique number from 1 to 8, the sample space is:
[tex]\( \text{Sample Space} = \{1, 2, 3, 4, 5, 6, 7, 8\} \)[/tex]
2. Define the Event:
The specific event we are considering is drawing the number 6. Therefore, the event set can be written as:
[tex]\( \text{Event Set} = \{6\} \)[/tex]
3. Determine the Complement of the Event:
The complement of an event is the set of all outcomes in the sample space that are not in the event set. This means we need to exclude the number 6 from the sample space.
4. Form Subset A:
Subset [tex]\( A \)[/tex] will consist of all numbers from the sample space except for the number 6. Therefore, remove 6 from the sample space [tex]\( \{1, 2, 3, 4, 5, 6, 7, 8\} \)[/tex].
5. List the Elements in Subset A:
Removing 6 from the sample space, we get:
[tex]\[ A = \{1, 2, 3, 4, 5, 7, 8\} \][/tex]
### Conclusion:
By following the steps outlined above, we determine that subset [tex]\( A \)[/tex] representing the complement of the event in which the number 6 is drawn from the bag is:
[tex]\[ A = \{1, 2, 3, 4, 5, 7, 8\} \][/tex]
Thus, the correct option is:
\[ \boxed{A = \{1, 2, 3, 4, 5, 7, 8\}} \
### Step-by-Step Solution
1. Identify the Sample Space:
The sample space in this context is the set of all possible outcomes when drawing a slip of paper from the bag. Since each slip contains a unique number from 1 to 8, the sample space is:
[tex]\( \text{Sample Space} = \{1, 2, 3, 4, 5, 6, 7, 8\} \)[/tex]
2. Define the Event:
The specific event we are considering is drawing the number 6. Therefore, the event set can be written as:
[tex]\( \text{Event Set} = \{6\} \)[/tex]
3. Determine the Complement of the Event:
The complement of an event is the set of all outcomes in the sample space that are not in the event set. This means we need to exclude the number 6 from the sample space.
4. Form Subset A:
Subset [tex]\( A \)[/tex] will consist of all numbers from the sample space except for the number 6. Therefore, remove 6 from the sample space [tex]\( \{1, 2, 3, 4, 5, 6, 7, 8\} \)[/tex].
5. List the Elements in Subset A:
Removing 6 from the sample space, we get:
[tex]\[ A = \{1, 2, 3, 4, 5, 7, 8\} \][/tex]
### Conclusion:
By following the steps outlined above, we determine that subset [tex]\( A \)[/tex] representing the complement of the event in which the number 6 is drawn from the bag is:
[tex]\[ A = \{1, 2, 3, 4, 5, 7, 8\} \][/tex]
Thus, the correct option is:
\[ \boxed{A = \{1, 2, 3, 4, 5, 7, 8\}} \
