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%.

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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.