Internet search sites compete for users because they sell ad

Internet search sites compete for users because they sell advertising space on their sites and can charge more if they are heavily used. Choose an Internet search attempt at random and let X be the site used. Here is the probability distribution for the site the search uses:

Site / Probability
Google / 0.66
Yahoo / 0.21
MSN / 0.07
Ask.com / 0.04
Others / ??

a) What is the probability that a search attempt is made at a site other than the leading four?

b) what is the probability that a search attempt is directed to a site other than Google?

c) Given that you know that the search was not made at Google, what is the probability that the site was at MSN?

Solution

Answer:

Let X denote the chosen site

X : google yahoo MSN Ask.com Others
p(x): 0.66 0.21 0.07 0.04 ??

a) The probability of choosing a site other than the leading four (Google, Yahoo,MSN, Ask,com) =

1- (0.66+0.21+0.07+0.04) = 1-0.98= 0.02

b) The probbaility of choosing a site other than Google = probability of choosing any other site = 0.21+0.07+0.04+0.02= 0.34

c) Given that the search was not made at Google, the probability that the chosen site was MSN = 0.07/ (0.21+0.07+0.04+0.02) = 0.07/0.34= 0.2058