Question

the table shows the distribution, by age, of a random sample of 3850 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.

$$1300 + 850+710=2860$$

Step2: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The total number of moviegoers is \(n = 3850\), and the number of moviegoers aged at least 25 is \(m = 2860\).

$$P=\frac{2860}{3850}$$

Simplify the fraction \(\frac{2860}{3850}\) by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 2860 and 3850 is 110.

$$P=\frac{2860\div110}{3850\div110}=\frac{26}{35}$$

Answer:

\(\frac{26}{35}\)