Use thegeometric probability distributionto solve the following problem.

On the leeward side of the island of Oahu, in a small village, about86%of the residents are of Hawaiian ancestry. Letn= 1, 2, 3, ... represent the number of people you must meet until you encounter thefirstperson of Hawaiian ancestry in the village.

(a)Write out a formula for the probability distribution of the random variablen. (Enter a mathematical expression.)

P(n) =

(b)Compute the probabilities thatn= 1,n= 2, andn= 3. (For each answer, enter a number. Round your answers to three decimal places.)

P(1) =

P(2) =

P(3) =

(c)Compute the probability thatn4.Hint:P(n4) = 1P(n= 1)P(n= 2)P(n= 3). (Enter a number. Round your answer to three decimal places.)

(d)What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry?Hint: Usefor the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.)

residents