The table shows the distribution, by age, of a random sample of 2860 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 less than 65. Age Distribution of Moviegoers Ages 12-24 Number 920 25-44 950 45-64 790 65-74 200 The probability is. (Type an integer or a simplified fraction.)
The table shows the distribution, by age, of a random sample of 2860 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 less than 65. Age Distribution of Moviegoers Ages 12-24 Number 920 25-44 950 45-64 790 65-74 200 The probability is. (Type an integer or a simplified fraction.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![The image presents a table and a probability question related to the age distribution of moviegoers. The table contains the following information:
**Age Distribution of Moviegoers:**
- Ages 12-24: 920 moviegoers
- Ages 25-44: 950 moviegoers
- Ages 45-64: 790 moviegoers
- Ages 65-74: 200 moviegoers
The total sample size is 2860 moviegoers, aged from 12 to 74.
**Problem Statement:**
The task is to find the probability, expressed as a simplified fraction, that a randomly selected moviegoer is younger than 65 years old.
**Solution Explanation:**
To find the probability, add the number of moviegoers in age groups under 65 (12-24, 25-44, and 45-64) and divide by the total number of moviegoers.
- Total number of moviegoers younger than 65: 920 + 950 + 790 = 2660
The probability that a randomly selected moviegoer is less than 65 years old is:
\[
\frac{2660}{2860}
\]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor.
**Final Output:**
The probability is \( \frac{133}{143} \).
(Type an integer or a simplified fraction.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e9a2685-2e8f-42fc-9b67-6f36e017459c%2F9d34b507-e6c2-4855-8d14-e0694b961d88%2F53vm6sk_processed.png&w=3840&q=75)
Transcribed Image Text:The image presents a table and a probability question related to the age distribution of moviegoers. The table contains the following information:
**Age Distribution of Moviegoers:**
- Ages 12-24: 920 moviegoers
- Ages 25-44: 950 moviegoers
- Ages 45-64: 790 moviegoers
- Ages 65-74: 200 moviegoers
The total sample size is 2860 moviegoers, aged from 12 to 74.
**Problem Statement:**
The task is to find the probability, expressed as a simplified fraction, that a randomly selected moviegoer is younger than 65 years old.
**Solution Explanation:**
To find the probability, add the number of moviegoers in age groups under 65 (12-24, 25-44, and 45-64) and divide by the total number of moviegoers.
- Total number of moviegoers younger than 65: 920 + 950 + 790 = 2660
The probability that a randomly selected moviegoer is less than 65 years old is:
\[
\frac{2660}{2860}
\]
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor.
**Final Output:**
The probability is \( \frac{133}{143} \).
(Type an integer or a simplified fraction.)
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