An internet search engine looks for a certain keyword in a sequence of independent sites. It is believed that 20% of the sites contain this keyword.

Compute the probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword.

I don't get how the answer is 0.4096?

Question

An internet search engine looks for a certain keyword in a sequence of independent sites. It is believed that 20% of the sites contain this keyword.

Compute the probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword.

I don't get how the answer is 0.4096?

anonymous · Answer

Grrrr, it's the "at least" that tripped me up. 

Answer = 1 - P(1st try) = P(2nd try) - P(3rd try) - P(4th try) = 1 - .1024 - 0.128 - 0.16 - .2