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 0.8 and 0.2, respectively. If the site visitor arrives from a search site, the probabilities of blue and green colors in the advertisement are 0.4 and 0.6, respectively. The proportions of visitors from affil- iates 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?

0.5

Step-by-step explanation:

We can designate our given parameters in a more simpler way for easy calculation;

Let use U to represent the event that the visitor came from affiliates

Let use V to represent the event that the visitor came from search sites

Let use W to represent the event that the web site color is blue

Let use X to represent the event that the web site color is green

The proportions of visitors from affiliates P(U)= 0.3

The proportions of visitors from search sites P(V)= 0.7

Given that:

If a site visitor arrives from an affiliate and the probability is blue color

P (W║U) = 0.8

If a site visitor arrives from an affiliate and the probability is green color

P (X ║U) = 0.2

If the site visitor arrives from a search site and  the probability is blue color P(W ║ V) = 0.4

If the site visitor arrives from a search site and  the probability is green color

P(X ║ V) = 0.6

The proportions of visitors from affiliates P(U)= 0.3

The proportions of visitors from search sites P(V)= 0.7

Using Baye's theorem to find  the probability that a visitor is from a search site given that the blue ad was viewed P (V ║ W); we have

P (V ║ W) =

P (V ║ W) =

P (V ║ W) =

P (V ║ W) =

P (V ║ W) = 0.5385

P (V ║ W ≅ 0.5

Hence, the probability that a visitor is from a search site given that the blue ad was viewed = 0.5