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 [tex]$A$[/tex]?
[tex]A=(3)[/tex]
[tex]A=\{1,3 ; 5,7\}[/tex]
[tex]A=\{1,2,3,4,5,7,8\}[/tex]
[tex]A=112,3,4,5,5,7,8\}[/tex]
Answer (1)
Identify the set of numbers from 1 to 8.
Remove the number 6 from the set.
The remaining numbers form subset A.
Subset A is 1 , 2 , 3 , 4 , 5 , 7 , 8 .
Explanation
Understand the problem We are given a set of numbers from 1 to 8, inclusive. We want to find the subset A that represents the complement of the event where the number 6 is drawn. This means we want to find the set of all numbers from 1 to 8, excluding 6.
Identify the numbers to include in subset A We start with the set of numbers from 1 to 8: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . We need to remove the number 6 from this set.
Construct subset A After removing 6, we are left with the set 1 , 2 , 3 , 4 , 5 , 7 , 8 . This is the subset A we are looking for.
State the final answer Therefore, subset A is 1 , 2 , 3 , 4 , 5 , 7 , 8 .
Examples
In probability, understanding complements is essential. For instance, if you're analyzing the likelihood of rolling a die and not getting a 6, you're dealing with the complement of rolling a 6. This concept is used in risk assessment, game design, and statistical analysis to determine the chances of an event not happening, which is just as important as knowing the chances of it happening. Knowing the complement helps in making informed decisions in various real-life scenarios.
