The table shows the distribution, by age, of a random sample of 3660 moviegoers ages 12-74. If one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, that the moviegoer is not in the $45-64$ age range.
Age Distribution of Moviegoers
\begin{tabular}{|c|c|}
\hline Ages & Number \\
\hline $12-24$ & 1100 \\
\hline $25-44$ & 1290 \\
\hline $45-64$ & 660 \\
\hline $65-74$ & 610 \\
\hline
\end{tabular}
The probability is
(Type an integer or a simplified fraction.)

Step 1 ：The total number of moviegoers is 3660.

Step 2 ：The number of moviegoers in the 45-64 age range is 660.

Step 3 ：To find the number of moviegoers not in the 45-64 age range, subtract the number of moviegoers in the 45-64 age range from the total number of moviegoers. This gives us \(3660 - 660 = 3000\).

Step 4 ：The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the event is that the moviegoer is not in the 45-64 age range. The total number of outcomes is the total number of moviegoers, which is 3660. The number of ways the event can occur is the number of moviegoers not in the 45-64 age range, which is 3000. So, the probability is \(\frac{3000}{3660} = 0.819672131147541\).

Step 5 ：The question asks for a simplified fraction. The decimal 0.819672131147541 can be expressed as the fraction \(\frac{50}{61}\).

Step 6 ：Final Answer: The probability that the moviegoer is not in the 45-64 age range is \(\boxed{\frac{50}{61}}\).