A CBS News poll conducted June 10 and 11, 2006, among 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 results are shown in the table below.

 	better	same	worse
Republican	38	104	44
Democrat	12	87	137
none	21	90	118


Express your answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).

If we randomly select one of the adults who participated in this study, compute:

P(Democrat) = 


P(worse) = 
0.459
Correct

P(worse|Democrat) = 


P(Democrat|worse) = 
0.458
Correct

P(Democrat and worse) = 
0.210
Correct


Let's go through the calculations step by step.

### 1. Total Number of Adults Surveyed:
First, we need to calculate the total number of people surveyed:

\[
\text{Total} = (38 + 104 + 44) + (12 + 87 + 137) + (21 + 90 + 118) 
\]
\[
\text{Total} = 186 + 236 + 229 = 651
\]

So, the total number of adults surveyed is 651.

### 2. \( P(\text{Democrat}) \):
To compute the probability that a randomly selected adult is a Democrat, we use the following formula:

\[
P(\text{Democrat}) = \frac{\text{Total number of Democrats}}{\text{Total number of adults}}
\]

The total number of Democrats is:
\[
12 + 87 + 137 = 236
\]

Now, the probability is:
\[
P(\text{Democrat}) = \frac{236}{651} = 0.362
\]

### 3. \( P(\text{worse|Democrat}) \):
The conditional probability \( P(\text{worse|Democrat}) \) is the probability that someone thinks the economy is "getting worse" given that they are a Democrat. This is calculated as:

\[
P(\text{worse|Democrat}) = \frac{\text{Number of Democrats who think the economy is worse}}{\text{Total number of Democrats}}
\]

The number of Democrats who think the economy is worse is 137. The total number of Democrats is 236, so:

\[
P(\text{worse|Democrat}) = \frac{137}{236} = 0.581
\]

### Final Answers:

- \( P(\text{Democrat}) = 0.362 \)
- \( P(\text{worse|Democrat}) = 0.581 \)

If you have any further questions or want more details, feel free to ask!

Here are 5 additional related questions for deeper exploration:
1. What is the probability that a randomly selected person is a Republican?
2. What is the probability that a person is unaffiliated with any party and thinks the economy is "getting better"?
3. What is the probability that someone is a Republican given they think the economy is "getting worse"?
4. What is the joint probability that a person is unaffiliated and thinks the economy is "about the same"?
5. What is the probability that someone thinks the economy is "getting better"?

**Tip:** Conditional probabilities can help refine broader probabilities by taking specific groups into account. Always calculate carefully!

A CBS News poll conducted June 10 and 11, 2006, among 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 results are shown in the table below. Express your answers as a decimal and round to the nearest 0.001. If we randomly select one of the adults who participated in this study, compute: P(Democrat), P(worse), P(worse|Democrat), P(Democrat|worse), and P(Democrat and worse).

Learn how to compute probabilities using real poll data from a CBS News survey. Understand the probability of being a Democrat, the likelihood of thinking the economy is getting worse, and how conditional probabilities apply. This problem covers essential probability concepts, including conditional and joint probabilities, suitable for Grades 10-12.

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