Question: Chapter 3: Probability (basic)\nScore: 3/4\nAnswered: 3/4\n\nQuestion 4\n\nA store manager gathers some demographic information from the store's customers. The following chart summarizes the age-related information they collected:\n\nAge Number of Customers\n< 20 88\n20-29 51\n30-39 59\n40-49 52\n50-59 93\n60 82\n\nOne customer is chosen at random for a prize giveaway. (Round answers to 4 decimal places.)\n\na. What is the probability that the customer is at least 30 but no older than 59?\n\nb. What is the probability that the customer is either older than 60 or younger than 40?\n\nc. What is the probability that the customer is at least 50?
1. **State the problem:** We have customer counts by age groups and want to find probabilities for certain age ranges when one customer is chosen at random.
2. **Calculate total number of customers:**
$$\text{Total} = 88 + 51 + 59 + 52 + 93 + 82 = 425$$
3. **a. Probability customer is at least 30 but no older than 59:**
This includes age groups 30-39, 40-49, and 50-59.
$$\text{Count} = 59 + 52 + 93 = 204$$
Probability:
$$P = \frac{204}{425} \approx 0.4800$$
4. **b. Probability customer is either older than 60 or younger than 40:**
Older than 60 means age \(\geq 60\), younger than 40 means age < 40.
Counts:
- Younger than 40: 88 (\(<20\)) + 51 (20-29) + 59 (30-39) = 198
- Older than 60: 82
Total count:
$$198 + 82 = 280$$
Probability:
$$P = \frac{280}{425} \approx 0.6588$$
5. **c. Probability customer is at least 50:**
Includes age groups 50-59 and \(\geq 60\).
$$\text{Count} = 93 + 82 = 175$$
Probability:
$$P = \frac{175}{425} \approx 0.4118$$
**Final answers:**
- a. $0.4800$
- b. $0.6588$
- c. $0.4118$