Two Web colors are used for a site advertisement. If a site visitor arrives from

Question

Two Web colors are used for a site advertisement. If a site visitor arrives from an affiliate, the probabilities of the blue or green colors being used in the advertisement are 0.6 and 0.4, respectively. If the site visitor arrives from a search site, the probabilities of blue and green colors in the advertisement are 0.1 and 0.9, respectively. The proportions of visitors from affiliates and search sites are 0.3 and 0.7, respectively. What is the probability that a visitor is from a search site given that the blue ad was viewed?

Explanation / Answer

By affiliate : blue 0.3×0.6 = 0.18 ; green 0.3×0.4 = 0.12
by search: blue 0.7×0.1 = 0.07 ; green 0.7×0.9 = 0.63
Proportion of blue read by search = 0.07/(0.07+0.18) = 0.28 which is numerically the same as the requested probability.

Answer 28 %

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