Let's solve the missing part of the question step-by-step based on the image you've uploaded.

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:

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.