a wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. the…
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.\n| | displeased | pleased |\n|--|--|--|--|\n| a footlong shoe | 4 | 6 |\n| a toes knows shoe | 4 | 6 |\nwhat is the probability that a randomly selected customer purchased a toes knows shoe given that the customer is displeased?\nsimplify any fractions.
Answer
Explanation:
Step1: Calculate total number of displeased customers
The number of displeased customers for A Footlong shoe is 4 and for A Toes Knows shoe is 4. So the total number of displeased customers is $4 + 4=8$.
Step2: Calculate the number of displeased customers who purchased A Toes Knows shoe
The number of displeased customers who purchased A Toes Knows shoe is 4.
Step3: Use the conditional - probability formula
The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of purchasing A Toes Knows shoe and $B$ is the event of being displeased, then $P(A|B)=\frac{\text{Number of customers who are displeased and bought A Toes Knows shoe}}{\text{Total number of displeased customers}}$. So the probability is $\frac{4}{8}=\frac{1}{2}$.
Answer:
$\frac{1}{2}$