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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 that purchased hiking shoes, and recorded the shoe brand and the customer's level of happiness. A Footlong shoe A Toes Knows shoe Displeased 4 3 Pleased 10 7 Very pleased 11 10 What is the probability that a randomly selected customer is pleased and purchased a Toes Knows shoe? Simplify any fractions.

Answer :

First, notice that we have the results of 45 surveys, then, if A is the event {the customer is pleased} and B is the evente {the customer purchased a Toes Knows shoes}, then their probabilities are:

[tex]\begin{gathered} P(A)=\frac{10+7}{45}=\frac{17}{45} \\ P(B)=\frac{3+7+10}{45}=\frac{20}{45} \end{gathered}[/tex]

then, the probability that both A and B occur is:

[tex]P(A\cap B)=P(A)\cdot P(B)=\frac{17}{45}\cdot\frac{20}{45}=\frac{340}{2025}=\frac{68}{405}[/tex]

therefore, the probability that a random selected customer is pleased and purchased a Toes Knows shoe is 68/405

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