Question

Suppose that on the leeward side of the island of Oahu, in the small village of Nanakuli, about 50% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3,… represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli. Compute the probability for 3. Round your answer to the nearest ten thousandth.

Answer 1

Let , the random variable 'N' represent the number of people meet until you encounter the first person of Hawaiian ancestry in the village of Nanakuli.

In the small village of Nanakuli 50% of the residents are of Hawaiian ancestry.

Random variable 'N' follows geometric distribution, with success probability P = 0.5

We have to find P( n = 3 )

Using formula of geometric distribution ,

P( N = n ) = ( 1 - P ) ^{n - 1} P    ,   n : 1 , 2 , 3 , ....

P( N = 3 ) = ( 1 - 0.5 )^3-1 ( 0.5 )

P( N = 3 ) = 0.125