Question

the table shows the distribution, by age, of a random sample of 3610 moviegoers ages 12 - 74. if one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, that the moviegoers age is at least 25. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the number of moviegoers aged at least 25

Add the number of moviegoers in the age - groups \(25 - 44\), \(45 - 64\), and \(65 - 74\).

$$1040+790 + 720=2550$$

Step2: Use the probability formula

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of moviegoers is \(n = 3610\), and the number of favorable outcomes (age at least 25) is \(m=2550\). So, \(P=\frac{2550}{3610}\).
Simplify the fraction \(\frac{2550}{3610}\) by dividing both the numerator and the denominator by \(10\) first: \(\frac{2550\div10}{3610\div10}=\frac{255}{361}\).
Check if \(255\) and \(361\) have a common factor. Since \(255 = 3\times5\times17\) and \(361=19\times19\), the fraction \(\frac{255}{361}\) is in its simplest form.

Answer:

\(\frac{255}{361}\)