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### Understanding the Problem:
We are working with a table representing the opinions of 651 adults regarding the economy and their political affiliation. The table provides data about whether people think the economy is getting better, staying the same, or getting worse, along with their affiliation (Republican, Democrat, or none).

**The table is as follows:**

| Affiliation   | Better | Same | Worse | Total |
|---------------|--------|------|-------|-------|
| Republican    | 38     | 104  | 44    | 186   |
| Democrat      | 12     | 87   | 137   | 236   |
| None          | 21     | 90   | 118   | 229   |
| **Total**     | 71     | 281  | 299   | 651   |

### Given Probabilities:
- P(worse) = 0.4594
- P(worse | affiliated with neither party) = 0.5153
- P(affiliated with neither party and worse) = 0.1815

### Problem (a):
**P(affiliated with neither party)**  
This is the probability that a randomly selected adult from the survey is not affiliated with either the Republican or Democratic parties (i.e., "none"). We will compute this as the ratio of people with no affiliation to the total number of people surveyed.

- Total people with no affiliation: 229
- Total number of people surveyed: 651

\[
P(\text{affiliated with neither party}) = \frac{229}{651}
\]

Let me calculate this.The probability that a randomly selected adult is affiliated with neither party (P(affiliated with neither party)) is approximately **0.3518**.

Would you like further details on the calculations or any clarification?

### Additional Questions:
1. How would you calculate the probability of someone affiliated with either party?
2. Can you explain the difference between conditional and joint probabilities in this context?
3. How can you use total probability to verify some of these values?
4. What is the probability of selecting someone who thinks the economy is getting better?
5. How would you compute P(affiliated with either party and thinks the economy is getting worse)?

### Tip:
When dealing with probability tables, always double-check the totals and ensure the sum of probabilities equals 1.

A CBS News poll involved a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican, or none) and their opinion of how the US economy was changing ('getting better', 'getting worse' or 'about the same'). The question asks to calculate probabilities such as P(affiliated with neither party) and P(worse).

In this problem, we calculate probabilities based on a CBS News poll asking adults about party affiliation and opinions on the economy. We cover how to compute P(affiliated with neither party), P(worse), and conditional probabilities using the data provided. Suitable for high school students learning probability theory.

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