Answer:
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) = [tex]\frac{P(W|V)P(V)}{P(W|U)P(U)+P(W|V)P(V)}[/tex]
P (V ║ W) = [tex]\frac{(0.4)(0.7)}{(0.8)(0.3)+(0.4)(0.7)}[/tex]
P (V ║ W) = [tex]\frac{0.28}{0.24+0.28}[/tex]
P (V ║ W) = [tex]\frac{0.28}{0.52}[/tex]
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
