A store manager gathers some demographic information from the store's customers. The following chart summarizes the age-related information they collected:
Age Number of Customers
<20 54
20−29 80
30−39 76
40−49 59
50−59 94
≥60 68
One customer is chosen at random for a prize giveaway.
a. What is the probability that the customer is at least 40 but no older than 59?
b. What is the probability that the customer is either older than 50 or younger than 30?
c. What is the probability that the customer is at least 50?
a. Well, we're looking for the probability that the customer is at least 40 but no older than 59. Let's add up the number of customers in those age groups: 59 (40-49) + 94 (50-59) = 153. Now, we need to find the total number of customers: 54 (<20) + 80 (20-29) + 76 (30-39) + 59 (40-49) + 94 (50-59) + 68 (≥60) = 431. The probability is the number of customers in the desired age range divided by the total number of customers: 153/431 ≈ 0.355.
b. To find the probability that the customer is either older than 50 or younger than 30, we need to add up the number of customers in those age groups: 94 (50-59) + 68 (≥60) + 54 (<20) + 80 (20-29) = 296. Again, we divide this by the total number of customers to get the probability: 296/431 ≈ 0.686.
c. The probability that the customer is at least 50 is the number of customers in that age group divided by the total number of customers: 94/431 ≈ 0.218.
To find the probability in these scenarios, we need to calculate the total number of customers in each age range and then divide it by the total number of customers.
a. To find the probability that the customer is at least 40 but no older than 59, we need to add up the number of customers in the age range 40-49 and 50-59 and divide it by the total number of customers.
Number of customers between 40-49 = 59
Number of customers between 50-59 = 94
Total number of customers = Sum of the number of customers in each age range = 54 + 80 + 76 + 59 + 94 + 68
Now, calculate the probability:
Probability = (Number of customers between 40-49 + Number of customers between 50-59) / Total number of customers
b. To find the probability that the customer is either older than 50 or younger than 30, we need to add up the number of customers in the age range < 20 and ≥ 60, and also the number of customers who are older than 50 but younger than 60. Then divide it by the total number of customers.
Number of customers < 20 = 54
Number of customers ≥ 60 = 68
Number of customers between 50-59 = 94
Now, calculate the probability:
Probability = (Number of customers < 20 + Number of customers ≥ 60 + Number of customers between 50-59) / Total number of customers
c. To find the probability that the customer is at least 50, we need to add up the number of customers in the age range 50-59 and ≥ 60 and divide it by the total number of customers.
Number of customers between 50-59 = 94
Number of customers ≥ 60 = 68
Now, calculate the probability:
Probability = (Number of customers between 50-59 + Number of customers ≥ 60) / Total number of customers
Remember to substitute the values of the total number of customers into the equations.