7A sporting goods company operates retail stores in the Orlando and Tampa areas.

Question

7A sporting goods company operates retail stores in the Orlando and Tampa areas. Customers were asked to rate their shopping experiences. The results indicated that 15% rated their shopping experience as Poor, 45% as Average and 40% as Good. In addition, 67% of the customers who rated their experience as Poor came from Tampa, 36% of the customers who rated their experience as Average came from Tampa and 30% of the customers who rated their experience as Good came from Tampa.

(a) What is the probability that a customer came from Tampa?

(b) What is the probability that a customer who shopped in Tampa rated his or her experience as Good?

Explanation / Answer

(a) What is the probability that a customer came from Tampa?

Solution:

We are given,

P(poor) = 0.15

P(average) = 0.45

P(good) = 0.40

P(Tampa with poor) = 0.67

P(Tampa with average) = 0.36

P(Tampa with good) = 0.30

Required probability = (0.15*0.67) + (0.45*0.36) + (0.40*0.30)

Required probability = 0.3825

(b) What is the probability that a customer who shopped in Tampa rated his or her experience as Good?

Solution:

We are given,

Probability that a customer shopped in Tampa = 0.3825

P(good) = 0.40

Required probability = 0.3825/0.40 = 0.95625

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