The camera department of a large department store sells three different brands o

Question

The camera department of a large department store sells three different brands of cameras: Proxima, Yakima, and Tetron. Approximately 60% of the cameras sold are Yakimas with Tetrons accounting for 30% of sales and Proxima the remaining 10%. Store records show that approximately 1/4 of those who purchase a Yakima return within one year to purchase accessories for their camera. The corresponding figures for the other two are: Tetron, 1/5; and Proxima, 3/5. If a person is known to have purchased an accessory within a year of the purchase of a camera, what is the probability the person purchased a Yakima?

Explanation / Answer

using P Y T to represent the cameras, we first need to find out how much of the whole purchasing population came back for an accessory. for P, which are 10% of the total customers, 60% returned (3/5) to purchase an accessory, multiply .10 x .60 to get .06 or 6% (who purchased P and returned to purchase an accessory) for Y: .60 x .25 = .15 for T: .30 x .20 = .06 So we have .06 and .15 and .06 as the percentages who bought an accessory. This totals up to .27, so 27% of the purchasing population returned to buy an accessory, regardless of which brand of camera they bought. .15 of this 27% bought the Y, which are the ones we are interested in. We need to find out how many percent of .27 that .15 is, so we divide .15 by .27 which equals .5555555 or 55.56%

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