Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The Seattle store does 50 percent of the total sales in a year, while the Portland store does 35 percent of the total sales. Further analysis indicates that of the sales in Seattle, 20 percent are in boat accessories. The percentage of boat accessories at the Portland store is 30 and the percentage at the Phoenix store is 25. If a sales dollar is recorded as a boat accessory, the probability that the sale was made at the Portland store is:
A) slightly greater than 0.43
B) 0.35
C) 0.2425
D) None of the above

Question

Quizplus · Accepted Answer

To find the probability that a sale was made at the Portland store given that it was a boat accessory sale, we use the formula for conditional probability. First, calculate the total percentage of sales that are boat accessories across all stores. For Seattle: $50\% \times 20\% = 10\%$, for Portland: $35\% \times 30\% = 10.5\%$, and for Phoenix (which must do 15% of the total sales since Seattle does 50% and Portland does 35%, leaving 15% for Phoenix): $15\% \times 25\% = 3.75\%$. The total percentage of sales that are boat accessories is $10\% + 10.5\% + 3.75\% = 24.25\%$. The probability that a boat accessory sale was made at the Portland store is the percentage of boat accessory sales from Portland divided by the total percentage of boat accessory sales, which is $10.5\% / 24.25\% \approx 0.433$, or slightly greater than 0.43.

Harrison Water Sports Has Three Retail Outlets: Seattle, Portland, and Phoenix