Help would be greatly appreciated Two Web colors, red and green, are used for a

Question

Help would be greatly appreciated

Two Web colors, red and green, are used for a site advertisement. If the site visitor arrives from an affiliate the probabilities of the red or green colors are 0.8 and 0.2 respectively. If the site visitor arrives from a search site the probabilities of the red or green colors are 0.4 and 0.6 respectively. The proportion 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 red advertisement was viewed?

Explanation / Answer

Let

R, G = red, green
A, S = affiliate, search site

As by Bayes' Rule,

P(R) = P(A) P(R|A) + P(S) P(R|S) = 0.3*0.8 + 0.7*0.4 = 0.52

Thus,

P(S|R) = P(S) P(R|S) / P(R) = 0.7*0.4/0.52 = 0.538461538 [ANSWER]

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