What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? (please round to four decimal places) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming? (please round to four decimal places) ### 2.17 Global warming: A research poll asked 1643 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies.| | Earth is warming | Not warming | Don't know (or refuse) | Total ||----------------------------|------------------|-------------|------------------------|-------|| **Conservative Republican**| 0.06 | 0.07 | 0.04 | 0.17 || **Mod/Lib Republican** | 0.12 | 0.02 | 0.07 | 0.21 || **Mod/Cons Democrat** | 0.15 | 0.01 | 0.07 | 0.23 || **Liberal Democrat** | 0.30 | 0.01 | 0.08 | 0.39 || **Total** | 0.63 | 0.11 | 0.26 | 1 |### Analysis:The table organizes respondents into four categories based on their political ideology: Conservative Republicans, Moderate/Liberal Republicans, Moderate/Conservative Democrats, and Liberal Democrats. Their responses to the question about global warming are broken down into three categories: "Earth is warming," "Not warming," and "Don't know (or refuse)."- **Conservative Republicans** represent 0.17 of the total respondents, with only 0.06 believing that the Earth is warming.- **Moderate/Liberal Republicans** make up 0.21 of the respondents, with 0.12 convinced that global warming is occurring.- **Moderate/Conservative Democrats** constitute 0.23 of the total, with 0.15 acknowledging global warming.- **Liberal Democrats** are the most likely to agree with the global warming statement, representing 0.39 of the total, with 0.30 affirming the warming trend.Across all political and ideological groups, 0.63 of the total respondents agree that the Earth is warming, 0.11 believe it is not warming, and 0.26 either don't know or refused to answer.Understanding these distributions

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What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? (please round to four decimal places) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming? (please round to four decimal places)

What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? (please round to four decimal places) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming? (please round to four decimal places)

A First Course in Probability (10th Edition)

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican? (please round to four decimal places)

What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming? (please round to four decimal places)

### 2.17 Global warming:

A research poll asked 1643 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies.

| | Earth is warming | Not warming | Don't know (or refuse) | Total |
|----------------------------|------------------|-------------|------------------------|-------|
| **Conservative Republican**| 0.06 | 0.07 | 0.04 | 0.17 |
| **Mod/Lib Republican** | 0.12 | 0.02 | 0.07 | 0.21 |
| **Mod/Cons Democrat** | 0.15 | 0.01 | 0.07 | 0.23 |
| **Liberal Democrat** | 0.30 | 0.01 | 0.08 | 0.39 |
| **Total** | 0.63 | 0.11 | 0.26 | 1 |

### Analysis:
The table organizes respondents into four categories based on their political ideology: Conservative Republicans, Moderate/Liberal Republicans, Moderate/Conservative Democrats, and Liberal Democrats. Their responses to the question about global warming are broken down into three categories: "Earth is warming," "Not warming," and "Don't know (or refuse)."

- **Conservative Republicans** represent 0.17 of the total respondents, with only 0.06 believing that the Earth is warming.
- **Moderate/Liberal Republicans** make up 0.21 of the respondents, with 0.12 convinced that global warming is occurring.
- **Moderate/Conservative Democrats** constitute 0.23 of the total, with 0.15 acknowledging global warming.
- **Liberal Democrats** are the most likely to agree with the global warming statement, representing 0.39 of the total, with 0.30 affirming the warming trend.

Across all political and ideological groups, 0.63 of the total respondents agree that the Earth is warming, 0.11 believe it is not warming, and 0.26 either don't know or refused to answer.

Understanding these distributions

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