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ealeql
02-25-2010, 02:56 PM
(I accidentally posted this in the statistics forum so I am moving it over here.)

I have worked on solving the problem below for over an hour and even went to a math major for help, but we were stumped. We thought we would divide total sales b boat accessories sales for each store and then add those figures together in the bottom of the equation. On the top we thought we would would use the data from the portland store (divide 30% of 35%), but this computer does not work.
Our computation was .105/.105 + .1 + .0375 (conditional probability)
I am not sure if we are doing this correctly and the reasoning behind it and explanation would be greatly appreciated.
Thanks,

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 is 25 at the Phoenix store. 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.

BGM
02-25-2010, 03:27 PM
Let E, F, G be the events that the sale was made at Seattle, Portland and Phoenix
B be the event that the sale is record as a boat accessory

Then P(E) = 0.5, P(F) = 0.35 and hence P(G) = 1 - P(E) - P(F) = 0.15
as {E, F, G} form a partition over the total sales
Also note P(B|E) = 0.2, P(B|F) = 0.3 and P(B|G) = 0.25

Using Bayes Theorem:
P(F|B)
= P(B|F)P(F)/[P(B|E)P(E) + P(B|F)P(F) + P(B|G)P(G)]
= (0.3)(0.35)/[(0.2)(0.5) + (0.3)(0.35) + (0.25)(0.15)]
= 0.105/(0.1 + 0.105 + 0.0375) = 42/97

ealeql
02-25-2010, 08:03 PM
Thank you. How did you think of using Bayes Theorem. Was there anything in the wording? I was trying to make various conditional charts and using weighted measures.

Outlier
02-25-2010, 08:50 PM
Our computation was .105/.105 + .1 + .0375
I got
10.5/[10 + {15/4} +10.5]
using a Venn diagram.