Question

the table shows the distribution, by age, of a random sample of 3450 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 25 - 44 age range.
the probability is
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the number of moviegoers not in 25 - 44 age range

The total number of moviegoers is \(n = 3450\). The number of moviegoers in the 25 - 44 age range is \(n_{25 - 44}=730\). The number of moviegoers not in the 25 - 44 age range is \(n_{\text{not }25 - 44}=3450 - 730=2720\).

Step2: Calculate the probability

The probability \(P\) that a moviegoer is not in the 25 - 44 age range is given by the formula \(P=\frac{n_{\text{not }25 - 44}}{n}\). Substitute \(n_{\text{not }25 - 44}=2720\) and \(n = 3450\) into the formula: \(P=\frac{2720}{3450}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 2720 and 3450 is 10. So \(P=\frac{2720\div10}{3450\div10}=\frac{272}{345}\).

Answer:

\(\frac{272}{345}\)