Question

let a be an event within the sample space s, and let n(a)=a and n(s)=s. use the complements principle of counting to find an expression for n(a).
n(a) =

Explanation:

Step1: Recall complements principle

The total number of elements in the sample - space $S$ is $n(S)=s$, and the number of elements in event $A$ is $n(A)=a$. The complement of event $A$, denoted as $A'$, consists of all elements in $S$ that are not in $A$.

Step2: Calculate $n(A')$

By the complements principle of counting, $n(A)+n(A') = n(S)$. So, we can solve for $n(A')$ by rearranging the equation: $n(A')=n(S)-n(A)$. Substituting $n(A) = a$ and $n(S)=s$, we get $n(A')=s - a$.

Answer:

$s - a$