A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. The consulting company gathered data from each customer who purchased hiking shoes, and recorded the shoe brand and the customer's level of happiness.Displeased PleasedA Footlong shoe 3 5A Toes Knows shoe 8 6A Toe-tastic shoe 3 8What is the probability that a randomly selected customer is displeased or did not purchase a Footlong shoe?Simplify any fractions.Submit
Question
A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. The consulting company gathered data from each customer who purchased hiking shoes, and recorded the shoe brand and the customer's level of happiness.Displeased PleasedA Footlong shoe 3 5A Toes Knows shoe 8 6A Toe-tastic shoe 3 8What is the probability that a randomly selected customer is displeased or did not purchase a Footlong shoe?Simplify any fractions.Submit
Solution
To solve this problem, we first need to calculate the total number of customers and the number of customers who are either displeased or did not purchase a Footlong shoe.
Step 1: Calculate the total number of customers The total number of customers is the sum of all the customers who purchased each type of shoe, whether they were pleased or displeased.
A Footlong shoe: 3 (displeased) + 5 (pleased) = 8 customers A Toes Knows shoe: 8 (displeased) + 6 (pleased) = 14 customers A Toe-tastic shoe: 3 (displeased) + 8 (pleased) = 11 customers
Total customers = 8 (Footlong) + 14 (Toes Knows) + 11 (Toe-tastic) = 33 customers
Step 2: Calculate the number of customers who are either displeased or did not purchase a Footlong shoe The number of displeased customers is the sum of the displeased customers who purchased each type of shoe.
Displeased customers = 3 (Footlong) + 8 (Toes Knows) + 3 (Toe-tastic) = 14 customers
The number of customers who did not purchase a Footlong shoe is the sum of the customers who purchased the other two types of shoes.
Customers who did not purchase a Footlong shoe = 14 (Toes Knows) + 11 (Toe-tastic) = 25 customers
However, since we are looking for customers who are either displeased or did not purchase a Footlong shoe, we need to make sure we are not double counting any customers. Since the displeased customers who did not purchase a Footlong shoe are already included in both the number of displeased customers and the number of customers who did not purchase a Footlong shoe, we need to subtract them once to get the correct total.
Displeased customers who did not purchase a Footlong shoe = 8 (Toes Knows) + 3 (Toe-tastic) = 11 customers
Total customers who are either displeased or did not purchase a Footlong shoe = 14 (displeased) + 25 (did not purchase Footlong) - 11 (double counted) = 28 customers
Step 3: Calculate the probability The probability that a randomly selected customer is displeased or did not purchase a Footlong shoe is the number of customers who are either displeased or did not purchase a Footlong shoe divided by the total number of customers.
Probability = 28 / 33 = 0.848 or 84.8% when expressed as a percentage.
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