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 customers level of happiness.

	a footlong shoe	a toes knows shoe
displeased	3	3
pleased	3	3

what is the probability that a randomly selected customer is pleased or purchased a toes knows shoe?
simplify any fractions.

Explanation:

Step1: Calculate total number of customers

Total customers \(=3 + 3+3 + 3=12\)

Step2: Calculate number of customers who are pleased or purchased a Toes Knows shoe

Number of pleased customers \(=3 + 3 = 6\)
Number of customers who purchased Toes Knows shoe \(=3+3 = 6\)
Number of customers who are pleased and purchased Toes Knows shoe \(=3\)
Using the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
Number of customers who are pleased or purchased a Toes Knows shoe \(=6 + 6-3=9\)

Step3: Calculate the probability

Probability \(=\frac{9}{12}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)