Question

the table shows the distribution, by age, of a random sample of 3170 moviegoers ages 12-74. if one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, that the moviegoer’s age is at least 25.
age distribution of moviegoers

ages	number
25-44	760
45-64	780
65-74	520

the probability is \boxed{}.
(type an integer or a simplified fraction.)

Explanation:

Step1: Find total number of moviegoers

Total number of moviegoers is given as 3170.

Step2: Find number of moviegoers aged at least 25

"At least 25" means ages 25 - 44, 45 - 64, and 65 - 74.
Sum their numbers: \(760 + 780 + 520 = 2060\)

Step3: Calculate probability

Probability = (Number of favorable outcomes) / (Total number of outcomes)
So, probability = \(\frac{2060}{3170}\)
Simplify the fraction by dividing numerator and denominator by 10: \(\frac{206}{317}\)

Answer:

\(\frac{206}{317}\)