Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 88 people in the 18-21 age bracket and finds that 75 of them respond and 13 refuse to respond. When 275 people in the 22-29 age bracket are contacted, 248 respond and 27 refuse to respond.

Assume that 1 of the 363 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond.

Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.

P(18-21 or agreed) =

%

(Hint: It might be helpful to organize the data into a table first.)

Let's organize the data into a table for clarity:

| Age Bracket     | Responded | Refused | Total  |
|-----------------|-----------|---------|--------|
| 18-21           | 75        | 13      | 88     |
| 22-29           | 248       | 27      | 275    |
| **Total**       | **323**   | **40**  | **363**|

### Given Information:
- The total number of people contacted is 363.
- We need to find the probability of selecting someone who is either:
  1. In the 18-21 age bracket, or
  2. Agreed to respond (from either age group).

This requires the union of two events:
- Event A: Person is in the 18-21 age bracket (88 people).
- Event B: Person agreed to respond (323 people).

#### Step 1: Find the total probability for the union of events.
Using the formula for the union of two events:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

- \( P(A) \) is the probability of selecting someone in the 18-21 age bracket: 
  \[
  P(A) = \frac{88}{363}
  \]

- \( P(B) \) is the probability of selecting someone who agreed to respond: 
  \[
  P(B) = \frac{323}{363}
  \]

- \( P(A \cap B) \) is the probability of selecting someone who is in the 18-21 age bracket and agreed to respond:
  \[
  P(A \cap B) = \frac{75}{363}
  \]

#### Step 2: Substitute the values into the formula.
\[
P(A \cup B) = \frac{88}{363} + \frac{323}{363} - \frac{75}{363}
\]

\[
P(A \cup B) = \frac{88 + 323 - 75}{363} = \frac{336}{363}
\]

#### Step 3: Convert the probability to a percentage.
\[
P(A \cup B) = \frac{336}{363} \approx 0.9256
\]
As a percentage, this is:
\[
P(A \cup B) \approx 92.6\%
\]

Thus, the probability of selecting someone in the 18-21 age bracket or someone who agreed to respond is **92.6%**.

---

Would you like any further details or clarification?

### Related Questions:
1. What is the probability of selecting someone in the 22-29 age bracket?
2. What is the probability of selecting someone who refused to respond?
3. What is the probability of selecting someone in the 18-21 age bracket who refused to respond?
4. How does the probability change if the number of respondents in the 22-29 age bracket increases by 10%?
5. What if the probability of refusal increased by 5% in each age bracket? How would the results change?

### Tip:
When calculating the probability of a union of two events, don't forget to subtract the overlap (intersection) to avoid double-counting.

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 88 people in the 18-21 age bracket and finds that 75 of them respond and 13 refuse to respond. When 275 people in the 22-29 age bracket are contacted, 248 respond and 27 refuse to respond. Assume that 1 of the 363 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the '%' symbol. P(18-21 or agreed) = %

Learn how to find the probability of selecting someone in the 18-21 age group or someone who agreed to respond in a survey. This detailed solution involves applying the union rule for probability with real-life data, suitable for Grades 9-12.

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