In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c). Purchase likelihood 18-34 35-44 45-54 55+ 209 308 322 403 29 7 25 14 Neither more nor less likely 280 202 159 133 Total 518 517 506 550 More likely Less likely Total 1242 75 774 2091 (a) What is the probability that a randomly selected individual is 45 to 54 years of age, given the individual is more likely to buy a product emphasized as "Made in our country"? The probability is approximately (Round to three decimal places as needed.)
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c). Purchase likelihood 18-34 35-44 45-54 55+ 209 308 322 403 29 7 25 14 Neither more nor less likely 280 202 159 133 Total 518 517 506 550 More likely Less likely Total 1242 75 774 2091 (a) What is the probability that a randomly selected individual is 45 to 54 years of age, given the individual is more likely to buy a product emphasized as "Made in our country"? The probability is approximately (Round to three decimal places as needed.)
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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![### Overview:
In a recent poll, a random sample of adults (18 years and older) was asked about their likelihood of purchasing a product when the advertisement emphasized "Made in our country." The responses were categorized by age group, as shown in the contingency table below.
### Contingency Table:
| Purchase likelihood | 18-34 | 35-44 | 45-54 | 55+ | Total |
|-----------------------------|-------|-------|-------|-----|--------|
| **More likely** | 209 | 308 | 322 | 403 | 1242 |
| **Less likely** | 29 | 7 | 25 | 14 | 75 |
| **Neither more nor less likely** | 280 | 202 | 159 | 133 | 774 |
| **Total** | 518 | 517 | 506 | 550 | 2091 |
### Question:
(a) What is the probability that a randomly selected individual is 45 to 54 years of age, given the individual is more likely to buy a product emphasized as "Made in our country"?
**Calculation for Probability:**
- To find the probability that an individual is 45 to 54 years of age given that they are more likely to buy a product, use the formula:
\[
P(\text{45-54 | More likely}) = \frac{\text{Number of 45-54 year olds more likely}}{\text{Total number more likely}}
\]
- Plug in the numbers:
\[
P(\text{45-54 | More likely}) = \frac{322}{1242} \approx 0.259
\]
Thus, the probability is approximately **0.259**.
(Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e5d1fcc-dc4e-459d-accd-b833757f73de%2Fa709af64-29bd-45f5-b3d5-50042479323d%2Ftf2born_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Overview:
In a recent poll, a random sample of adults (18 years and older) was asked about their likelihood of purchasing a product when the advertisement emphasized "Made in our country." The responses were categorized by age group, as shown in the contingency table below.
### Contingency Table:
| Purchase likelihood | 18-34 | 35-44 | 45-54 | 55+ | Total |
|-----------------------------|-------|-------|-------|-----|--------|
| **More likely** | 209 | 308 | 322 | 403 | 1242 |
| **Less likely** | 29 | 7 | 25 | 14 | 75 |
| **Neither more nor less likely** | 280 | 202 | 159 | 133 | 774 |
| **Total** | 518 | 517 | 506 | 550 | 2091 |
### Question:
(a) What is the probability that a randomly selected individual is 45 to 54 years of age, given the individual is more likely to buy a product emphasized as "Made in our country"?
**Calculation for Probability:**
- To find the probability that an individual is 45 to 54 years of age given that they are more likely to buy a product, use the formula:
\[
P(\text{45-54 | More likely}) = \frac{\text{Number of 45-54 year olds more likely}}{\text{Total number more likely}}
\]
- Plug in the numbers:
\[
P(\text{45-54 | More likely}) = \frac{322}{1242} \approx 0.259
\]
Thus, the probability is approximately **0.259**.
(Round to three decimal places as needed.)
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